TWI403861B - Calculation method, generation method, program, exposure method, and mask fabrication method - Google Patents

Abstract

The present invention provides a calculation method of calculating, by a computer, a light intensity distribution formed on an image plane of a projection optical system, comprising a step of dividing an effective light source formed on a pupil plane of the projection optical system into a plurality of point sources, a step of shifting a pupil function describing a pupil of the projection optical system for each of the plurality of point sources in accordance with positions thereof, thereby generating a plurality of shifted pupil functions, a step of defining a matrix including the plurality of pupil functions, a step of performing singular value decomposition of the matrix, thereby calculating an eigenvalue and an eigenfunction, and a step of calculating the light intensity distribution, based on a distribution of the light diffracted by the pattern of the mask, and the eigenvalue and the eigenfunction.

Description

Calculation method, generation method, program, exposure method, and mask manufacturing method

The present invention relates to a calculation method, a production method, a program, an exposure method, and a mask manufacturing method.

A semiconductor device is manufactured by using a photolithography method by projecting and transferring a circuit pattern formed on a mask (or a photomask) onto a substrate such as a wafer via a projection optical system. With the recent progress in micropatterning of semiconductor devices, it is desirable for the projection exposure apparatus to further improve the resolution (to achieve higher resolution).

As means for achieving higher resolution of the projection optical system, a higher NA projection optical system (increasing the numerical aperture (NA) of the projection optical system) and shortening the exposed light are generally implemented. And RET (resolution enhancement technique) which improves the resolution of the projection optical system by lowering the k1 factor (also referred to as "process constant") has also received much attention.

The smaller the k1 factor, the higher the exposure difficulty. Conventionally, it has been measured that the exposure conditions of the circuit pattern can be faithfully projected by repeating the test a plurality of times. That is, exposure (such as exposure conditions and exposure methods) has been optimized. However, with the increasing difficulty of exposure, the detection of exposure conditions based on experiments requires long time and high cost. To solve this problem, for example, repeated exposure simulation by computer to optimize exposure conditions has become mainstream. The mainstream of analog technology is the so-called model-based RET, which performs simulations based on optical solid models.

The model-based RET is roughly calculated using partial homology images. The improved speed of partial coherent image calculations can reduce the time it takes for the model to be based on RET. At present, with the advancement of the computer environment, the calculation speed is improved by using a plurality of computers to form a parallel processing system. Techniques for improving computational speeds that are more efficient than using a computer to form a parallel processing system have also been proposed by performing an improved algorithm for partial coherent image computation.

For example, the calculation of the name SOCS is indicated in "Full-chip Lithography Simulation and Design Analysis-How OPC is changing IC Design" by Cris Spence, Proceedings of SPIE, USA, SPIE Press, 2005 Vol. 5751, pp. 1-14. The method increases the speed of the calculation (simulation speed) to 10,000 times the previous one. Moreover, Alfred Kwok-Kit Wong's "Optical Imaging in Projection Microlithography", USA, SPIE press, 2005, pp. 151-163, illustrates partial homomorphic imaging calculations, but does not mention that the calculation speed is higher than the calculation speed obtained using the SOCS algorithm. Algorithm. It is to be noted that Alfred Kwok-Kit Wong, "Optical Imaging in Projection Microlithography", U.S.A., SPIE press, 2005, pp. 151-163, regards SOCS as coherent decomposition.

Unfortunately, SOCS requires a lot of time to calculate the TCC (Transmission Intersection Technique) and decompose it into an eigenvalue and an eigenfunction.

The present invention provides a calculation method that can calculate the TCC of an exposure apparatus in a short period of time. The present invention provides a calculation method that calculates a light intensity distribution formed on an image plane of a projection optical system in a short period of time. The present invention provides a method of generating a pattern material of a mask in a short period of time.

According to a first aspect of the present invention, there is provided a calculation method for calculating a light intensity formed on an image plane of a projection optical system by a computer when an illumination optical system is used to illuminate a mask and an image of a pattern of a mask is projected through the transmission optical system a distribution comprising a dividing step of dividing an effective light source formed on a pupil plane of the projection optical system into a plurality of point light sources, generating a step of moving light describing the projection optical system for each of the plurality of point light sources and according to their positions a pupil function of the pupil, thereby generating a plurality of moving pupil functions, defining steps, defining a matrix comprising a plurality of pupil functions generated in the generating step, the first calculating step, performing singular value decomposition of the matrix, borrowing The calculating the eigenvalue and the eigenfunction, and the second calculating step, calculating the light formed on the image plane of the projection optical system based on the light intensity distribution and the eigenvalue and the eigenfunction diffracted by the pattern of the mask Intensity distribution.

According to a second aspect of the present invention, there is provided a method of generating a material for generating a pattern of a mask for an exposure apparatus including a projection optical system by a computer, comprising a dividing step formed on a pupil plane of the projection optical system The effective light source becomes a plurality of point light sources, and the generating step moves a pupil function describing the pupil of the projection optical system for each of the plurality of point light sources according to the position of the point light sources, thereby generating a plurality of moving pupil functions, a defining step of defining a matrix comprising a plurality of pupil functions generated in the generating step, a first calculating step, performing a singular value decomposition of the matrix defined in the defining step, thereby calculating an eigenvalue and an eigenfunction, a second calculating step of calculating, based on the distribution of light diffracted by the target pattern and the eigenvalues and eigenfunctions calculated in the first calculation step, when the elements of the target pattern are inserted onto the object plane of the projection optical system An image indicating that elements interact with each other, and a data generation step that generates a mask based on the image calculated in the second calculation step Data pattern.

According to a third aspect of the present invention, there is provided a storage medium for storing a program for causing a computer to perform calculation when an illumination optical system is used to illuminate a mask and project an image of the mask pattern onto the substrate via the projection optical system. The light intensity distribution on the image plane of the projection optical system causes the computer to perform the dividing step, and divides the effective light source formed on the pupil plane of the projection optical system into a plurality of point light sources, and generates steps according to the position of the point light source. Each of the plurality of point sources moves a pupil function describing the pupil of the projection optical system, thereby generating a plurality of moving pupil functions, defining steps, defining a matrix including a plurality of pupil functions generated in the generating step, first a calculating step of performing a singular value decomposition of the matrix defined in the defining step, thereby calculating an eigenvalue and an eigenfunction, and a second calculating step, based on the distribution of light diffracted by the pattern of the mask, and An eigenvalue and an eigenfunction calculated in a calculation step are calculated on the image plane of the projection optical system The light intensity distribution.

According to a fourth aspect of the present invention, a storage medium storing a program for causing a computer to execute processing for generating a pattern of a mask for an exposure device including a projection optical system, the program causing a computer to perform a segmentation step, and dividing into a projection The effective light source on the pupil plane of the optical system becomes a plurality of point light sources, and the generating step moves the pupil function describing the pupil of the projection optical system for each of the plurality of point light sources according to the position of the point light source, thereby generating a plurality of movements a pupil function, a defining step, defining a matrix comprising a plurality of pupil functions generated in the generating step, a first calculating step, performing a singular value decomposition of the matrix defined in the defining step, thereby calculating the eigenvalue and the present a sign function, a second calculating step, when inserting an element of the target pattern onto the object plane of the projection optical system, based on a distribution of light diffracted by the target pattern and an eigenvalue and a value calculated in the first calculating step a function, an image representing the influence of elements on each other, and a data generation step based on the second calculation step Count of image data to generate the mask pattern.

According to a fifth aspect of the present invention, there is provided an exposure method comprising a calculation step of calculating a projection optical system when an illumination optical system is used to illuminate a mask and project an image of the pattern of the mask onto the substrate via the projection optical system The light intensity distribution on the image plane, the adjusting step, adjusting the exposure condition based on the calculated light intensity distribution in the calculating step, and the exposing step, after the adjusting step, projecting the image of the mask pattern onto the substrate; the calculating step includes dividing a step of dividing the effective light source formed on the pupil plane of the projection optical system into a plurality of point light sources, and generating a step of moving a pupil function describing the pupil of the projection optical system for each of the plurality of point light sources according to the position of the point light source, Thereby generating a plurality of moving pupil functions, defining steps, defining a matrix comprising a plurality of pupil functions generated in the generating step, a first calculating step, performing singular value decomposition of the matrix defined in the defining step, thereby Calculating the eigenvalue and the eigenfunction, and the second calculation step, based on the mask by the mask The distribution of the diffracted light, and a first step in calculating the eigenvalues and the eigenfunctions calculated in calculating the projected light intensity of the image formed plane of the optical distribution system.

According to a sixth aspect of the present invention, there is provided a mask manufacturing method comprising: generating data of a pattern for a mask by the above-described generating method, and fabricating a mask using the generated data.

According to a seventh aspect of the present invention, there is provided an exposure method comprising the steps of: manufacturing a mask made by a mask, illumination by the mask manufacturing method, and projecting an image of a pattern of a mask via a projection optical system Above the substrate.

According to an eighth aspect of the present invention, there is provided a method for calculating a transmission intersection coefficient calculated by a computer in an exposure apparatus, the exposure apparatus illuminating the mask using the illumination optical system, and projecting an image of the pattern of the mask to the substrate via the projection optical system The calculation method includes a dividing step of dividing the effective light source formed on the pupil plane of the projection optical system into a plurality of point light sources, and generating a step of moving the light describing the projection optical system for each of the plurality of point light sources according to the position of the point light source a pupil function, thereby generating a plurality of moving pupil functions, defining steps, defining a matrix comprising a plurality of pupil functions generated in the generating step, and calculating steps based on the matrix defined in the defining step Transmission intersection coefficient.

Further features of the present invention will be apparent from the description of the accompanying drawings.

The preferred embodiments of the present invention are described below with reference to the accompanying drawings. Throughout the drawings, the same reference numerals are used to refer to the same elements and are not repeated.

For example, the present invention is applicable to optical system imaging calculations based on partial homology imaging (partial coherence imaging calculation) in, for example, an exposure apparatus and a microscope. The present invention is also applicable to the generation of mask materials for micromachines and for manufacturing various devices such as semiconductor wafers such as ICs and LSIs, display devices such as liquid crystal panels, detecting devices such as magnetic heads, and image senses. Measuring device such as CCD. Micromechanical herein refers to a technique of manufacturing a micro-scale complex mechanical system by applying a semiconductor integrated circuit manufacturing technique to the fabrication of a microstructure or a mechanical system itself.

The concepts disclosed in the present invention can be mathematically modeled. Thus, the present invention can be implemented as a software function of a computer system. In this embodiment, the software functions of the computer system include stylization with executable software encoding and performing partial homology imaging calculations. The software coding is performed by a processor of the computer system. During the software encoding operation, the stored code or related data is recorded in the computer platform. However, software coding systems are often stored in other locations or loaded into appropriate computer systems. The retentive software is encoded in at least one computer readable medium as one or more modules. The content of the invention may be described in the form of a code as described above, which may be used as one or a plurality of software products.

First, the coordinate system of the exposure apparatus according to this embodiment will be explained. In this embodiment, the coordinate systems in the exposure apparatus are roughly classified into two categories.

The first landmark system is defined on the surface of the mask (the object plane of the projection optical system) and the coordinates of the wafer surface (the image plane of the projection optical system), which is represented by (x, y) in this embodiment. By the magnification of the projection optics, the pattern size on the mask surface is different from the pattern size on the wafer surface. For the sake of simplicity, the ratio between the pattern size on the mask surface and the pattern size on the wafer surface is set by multiplying the pattern size on the surface of the mask and the magnification of the projection optical system in the following description. 1:1. Because of this setting, the ratio between the coordinate system on the surface of the mask and the coordinate system on the surface of the wafer also becomes 1:1.

The second coordinate system defines the coordinates on the pupil plane of the projection optical system, which is denoted by (f, g) in this embodiment. Assuming that the pupil size of the projection optical system is 1, the coordinates (f, g) on the pupil plane of the projection optical system are defined by a normalized coordinate system.

In the exposure apparatus, when no mask is inserted into the plane of the object of the projection optical system, the light intensity distribution formed on the pupil plane of the projection optical system is an effective light source, in this embodiment, S(f, g) indicates. In this embodiment, the pupil of the projection optical system is represented by the pupil function P(f, g). In general, the pupil function can include polarization effects (information) and polarization of the pupil characteristics. Even in this embodiment, the pupil function P(f, g) may include aberration effects and polarization of the pupil characteristics.

The exposure device illuminates the mask by partially coherent illumination and projects the mask pattern (mask pattern) onto the wafer. In this embodiment, the mask pattern includes information about the transmission and a phase defined by o(x, y), and a light intensity distribution (spatial image) formed on the surface of the wafer by I(x, y). The amplitude of the light diffracted by the mask pattern is defined by the projection optical system, and is represented by a(x, y) in this embodiment.

A conventional partial homology imaging calculation will now be described. The conventional partial homomorphic imaging calculations (calculating the light intensity distribution on the image plane of the projection optical system) can be roughly classified into three categories.

The first calculation is the so-called Abbe method. More specifically, Abbey calculates the light intensity I(x, y) by:

Where N ₁ is the number of point sources for numerical calculation, and F is Fourier transform.

The second calculation method calculates the TCC without eigenvalue decomposition. TCC is defined by the following formula:

Referring to equation (2), the TCC is provided by a four-dimensional function. Using TCC, the light intensity distribution I(x, y) can be calculated by:

Where N ₂ is a usable value of i, j, k and 1, and it depends on the number of pupil divisions for numerical calculation.

The third calculation method is a so-called SOCS that decomposes the TCC represented by the equation (2) into a plurality of eigenvalues and an eigenfunction. The light intensity distribution I(x, y) is calculated by the following formula:

Where λ _i is the ith eigenvalue, Ψ _i is the ith eigenfunction, and N ₃ is the number of point sources for the numerical calculation.

Abefa is suitable for small-scale calculations (small-scale simulation). More specifically, the Abbe method is applicable to the simulation of the relevant partial mask and to the change in the performance of the test image when changing optical settings such as effective light source, aberrations and polarization.

Using the calculation method of TCC, that is, using the calculation method of equation (3), the calculation speed is lower than the calculation speed of Abbe and SOCS, because quadrupole integration must be performed in equation (3). To calculate the light intensity distribution without using quadrupole integration in equation (3), SOCS can be used. SOCS is suitable for large-scale computing (large-scale simulation).

In large scale calculations, partial homomorphic imaging calculations are performed by dividing the mask into several regions. If the optical setting is not changed, the TCC shown by equation (2) will not change and the eigenfunction Ψ _i in equation (4) will not change. It is only necessary to repeat the simple calculation later, so SOCS is suitable for large-scale calculation. . However, SOCS is not suitable for small-scale calculations.

As understood by equation (2), because quadratic integration must be performed to calculate the TCC (ie, the TCC is provided by a four-dimensional function), the SOCS requires more time to calculate the TCC and requires a large amount of computer memory. SOCS also requires a lot of time to calculate the eigenvalue λ _i and the eigenfunction Ψ _i . In addition, if the optical setting is changed, the TCC must be calculated again in the SOCS. In summary, the SOCS system is not suitable for testing changes in imaging performance due to changing optical settings.

As mentioned above, conventional calculation methods require a large amount of simulation time. Further, in the prior art, it is necessary to selectively use the Abbe method and the SOCS according to the calculation target (that is, the small-scale calculation or the large-scale calculation performed).

1 is a schematic block diagram showing the configuration of a processing device 1 that performs a calculation method in accordance with the present invention.

As shown in FIG. 1, the processing device 1 is formed by, for example, a general-purpose computer, and includes a bus bar 10, a control unit 20, a display unit 30, a storage unit 40, an input unit 50, and a media interface 60.

The bus bar 10 interconnects the control unit 20, the display unit 30, the storage unit 40, the input unit 50, and the media interface 60.

The control unit 20 is formed by a CPU, a GPU, a DSP, or a microcomputer, and includes a cache memory for temporary storage.

The display unit 30 is formed of, for example, a display device such as a CRT display or a liquid crystal display.

The storage unit 40 is formed of, for example, a memory or a hard disk. In this embodiment, the storage unit 40 stores the pattern data 401, the effective light source information 402, the NA information 403, the lambda information 404, the aberration information 405, the polarization information 406, and the photoresist information 407. The storage unit 40 also stores a P operator 408, a spatial image 409, a mask data 410, and a spatial image calculation program 411.

The pattern material 401 is, for example, a material (a layout pattern or a target pattern) for designing a pattern of a layout in an integrated circuit.

The effective light source information 402 is a light intensity distribution (effective light source) formed on the pupil plane of the projection optical system of the exposure apparatus.

The NA information 403 is related to the numerical aperture of the projection optical system of the exposure device on the image side.

The lambda information 404 is related to the wavelength of light (exposure light) emitted by the light source of the exposure device.

The aberration information 405 is related to the aberration of the projection optical system of the exposure device.

The polarization information 406 is related to the polarized light (polarization state of the illumination light) formed by the illumination device (illumination optical system) of the exposure device.

Photoresist information 407 is related to the photoresist applied to the wafer.

The P operator 408 is a necessary matrix for calculating a spatial image as a light intensity distribution formed on the surface of the wafer (i.e., for the spatial image calculation program 411), which will be described in detail below.

The spatial image 409 is a result of calculating a spatial image (light intensity distribution) by the spatial image calculation program 411.

The mask data 410 is the material of the actual mask (mask). The mask data 410 is substantially different from the pattern data 401.

The spatial image calculation program 411 is a program for calculating a spatial image (light intensity distribution).

The input unit 50 includes, for example, a keyboard or a mouse.

The media interface 60 includes, for example, a floppy disk drive, a CD-ROM drive, and a USB interface, and is connectable to the storage medium 70. The storage medium 70 includes, for example, a floppy disk, a CD-ROM, and a USB memory.

The spatial image 409 is calculated by the spatial image calculation program 411 by specifically explaining the P operator 408. It is to be noted in this embodiment that λ represents the wavelength of the light for exposure, and NA represents the numerical aperture of the projection optical system for image measurement. It is also noted that σ represents the ratio of the numerical aperture of the illumination light that is directed from the illumination optics to the surface of the mask to the numerical aperture of the object of the projection optics.

The mask pattern and the spatial image in the exposure device have a partial coherent imaging relationship. As described above, the partial homology imaging calculation system is roughly classified into three categories (see equations (1), (3), and (4)). Since the Fourier transform F is used in the equations (1) and (4), the sum of the plane waves forms a spatial image from the viewpoint of Fourier optics. Each plane wave is represented by an index [-i2π(fx+gy)]. Although the Fourier transform F is not clearly shown in the equation (3), the sum of the plane waves similarly forms a spatial image because the index [-i2π(fx+gy)] is included therein.

Thus, from an optical point of view, the partial homology imaging is based on the plane wave index [-i2π(fx+gy)]. On the other hand, from a mathematical point of view, the exponent [-i2π(fx+gy)] is defined by an orthogonal function system. In this embodiment, the plane wave is defined by the orthogonal function system, whereby the spatial image 409 in the shorter time period can be calculated.

First, the case of calculating a one-dimensional space image (light intensity distribution) will be described. In this case, a plane wave can be expressed by an index (-i2π fx). The following equation vector defines the orthogonal function system:

Which When M is the number of divisions of f.

The P operator 408 will now be explained. Since it is assumed in this embodiment that M in the formula (5) is 7, f ₁ = -2, f ₂ = -4/3, f ₃ = -2/3, f ₄ =0, f ₅ = 2/3 , f ₆ = 4/3 and f ₇ = 2, as shown in FIG. 2. Fig. 2 is a diagram schematically showing a one-dimensional plane wave (orthogonal function system).

The light distribution (diffracted light distribution) diffracted by the mask pattern can be expressed by the (f _i ) index (-i2πf _i x). Then, the vector ∣Φ'> of the diffracted light distribution can be expressed as follows:

Wherein A is a diagonal matrix having an amplitude a(f _i ) of diffracted light as a diagonal element.

When the projection optical system is not aberrational, In its complete range its aperture has the function of passing a diffracted light component and shielding the diffracted light component in the range of ∣f∣>1. The output light at one point f' on the effective light source corresponds to the pupil movement of the projection optical system by f'. Therefore, when the light emitted from a point f' on the effective light source is diffracted by the mask pattern, The diffracted light component in the range passes through the pupil of the projection optical system, and the pupil of the projection optical system shields the diffracted light component in the range of ∣f-f'∣>1.

For example, if the light emitted by f=f ₄ =0 from the effective light source is diffracted by the mask pattern and blocked by the diaphragm of the projection optical system, the following equation can be used to indicate the aperture transmitted through the projection optical system. The amplitude of the diffracted light ∣Φ ₁ >:

∣Φ ₁ 〉=(0011100) A ∣Φ> ...(7)

The light intensity distribution on the surface of the wafer is obtained by calculating the square of the absolute value of the amplitude of the diffracted light transmitted through the pupil of the transmission optical system. Therefore, the light intensity distribution I ₁ (x) formed on the surface of the wafer by the point source f=f ₄ =0 can be expressed by the following formula:

I ₁ (x)=<Φ ₁ ∣Φ ₁ 〉 ...(8)

Wherein <Φ ₁ | based |Φ _1> conjugate transpose of (with) a matrix.

Similarly, if the light emitted from f=f ₃ on the effective light source is diffracted by the mask pattern and stopped by the pupil of the projection optical system, the following formula represents the diffracted light transmitted through the pupil of the projection optical system. Amplitude ∣Φ ₂ >:

∣Φ ₂ 〉=(0001110) A ∣Φ> ...(9)

Therefore, the light intensity distribution I ₂ (x) formed on the surface of the wafer by the point source f=f ₃ can be expressed by the following formula:

I ₂ (x)=<Φ ₂ ∣Φ ₂ 〉 (10)

And, the visual part of the coherent illumination is a set of different point sources. For example, suppose there are two point sources on the effective source, and the coordinates of these point sources are f=0 and f=f ₃ . Since the two point sources are different, the equation I ₁ (x) + I ₂ (x) (that is, the sum of the light intensities on the surface of the wafer) indicates that the two points originate from the light formed on the surface of the wafer. Intensity distribution.

The following formula defines the P operator P _1D :

Referring to equation (11), each column of the P operator P _1D moves the vector of the pupil of the projection optical system in accordance with the position of each point source on the effective light source plane. More specifically, the pupil of the projection optical system only needs to be moved by the difference between the central position on the pupil plane of the projection optical system and the position of each point source. Using the P operator P _1D , the light intensity distribution I(x) formed on the surface of the wafer can be expressed as follows:

It should be noted that the symbol "+" represents the transposed conjugate matrix of a matrix. Referring to the formula (12), the light intensity distribution I(x) is I ₁ (x) + I ₂ (x). In other words, the use of the P operator P _1D simplifies the representation of a spatial image formed on the surface of the wafer as a distribution of light intensity.

The formula (12) can be rewritten into the following formula:

I(x)=<Φ'| T _1D |Φ'〉 ...(13)

T _1D is a matrix defined by the following formula:

The matrix T _1D defined by the equation (14) illustrates the TCC. To calculate P _1D , it is only necessary to move the pupil of the projection optics without multiplication and addition. This makes it possible to calculate P _1D in a shorter period of time. Still preferably, since the TCC can be calculated by multiplying P _1D and its transposed conjugate, the P operator 408 is used to calculate the TCC faster than using Equation (2).

It should be noted that P _1D is not a square matrix. Rewrite P _1D to the following using singular value decomposition:

P _1D = WSV ...(15)

Where S is a diagonal matrix, and W and V are a single matrix. Substituting equation (15) into equation (12) and solving the singular value decomposition theorem using W ⁺ W as the identity matrix yields the following equation:

The SOCS, which is a conventional partial homomorphic imaging calculation method, decomposes the TCC into a cost eigenvalue and an eigenfunction, as described above. Because TCC is a very large matrix, a lot of time and large memory is required to calculate the TCC. In addition, a large amount of time is required to decompose the TCC into a levy value and an eigenfunction.

In this embodiment, singular value decomposition is performed for P operator 408. Referring to equation (14), since the elements of the P operator 408 are obviously less than the elements of the TCC, the P operator 408 performs less singular value decomposition than the TCC. In addition, since the calculation of the P operator does not require multiplication and addition, the P operator 408 can be calculated in a relatively short period of time. In other words, the P operator 408 is used to calculate the eigenvalue and eigenfunction with a smaller amount of computation and a smaller memory capacity than the SOCS. This makes it possible to calculate a spatial image 409 as a light intensity distribution formed on the surface of the wafer in a shorter period of time. Also, the formula (14) is used to calculate the TCC in a shorter period of time.

The case of calculating a one-dimensional space image (light intensity distribution) has been described above, and the case of calculating a two-dimensional space image (light intensity distribution) will be described below.

Let (f _i , g _j ) be the coordinates on the pupil plane of the discrete projection optical system. It should be noted that the range of i and j is from 1 to M. The vector ∣Φ' _2D > of the diffracted light distribution is represented by a one-dimensional matrix of elements of the following formula:

To specify ∣Φ' _2D >, "bottom" means the fraction after omitting the decimal point.第's Φ' _2D > system a(f _i , g _j ) index [-i2π(f _i x+g _j y)] assumes j = bottom surface [(n-1)/M]+1 and i= N-(j-1)×M. In this way, a two-dimensional orthogonal function system is obtained.

Let (f ₁ , g ₁ ) be the coordinate of the first point source on the effective light source, and the output light from the first point source is equivalent to the moving light describing the pupil of the projection optical system by (f ₁ , g ₁ ) The function P(f, g). The pupil function P ₁ (f, g) acting on the diffracted light is represented by P(f + f ₁ , g + g ₁ ). The elements of the pupil function P ₁ (f, g) are arranged one-dimensionally, as shown in the equation (17). Therefore, the pupil function P ₁ (f, g) can be expressed as a one-dimensional vector:

_{P 1 = (P 1 (f} 1, g 1) P 1 (f 2, g 1) ... P 1 (f M, g 1) P 1 (f 1, g 2) ... p 1 (f M, g M )))(18)

In order to explain P _l in detail, "bottom surface" means a fraction after omitting the decimal point. The first n lines P _{1 P 1 (f i, g j} ) a bottom surface assuming j = [(n-1) / M ] +1 and i = n- (j-1) × M. In this way, a two-dimensional orthogonal function system is obtained.

So that (f _2, g ₂₎ is a coordinate of the second point source on the effective light source, in the (f _2, g ₂₎ Mobile P (f, g) of the resulting _{P (f + f 2, g} + g 2) Indicates the pupil function P ₂ (f, g) acting on the light emitted from the second point source. Like the pupil function P ₁ (f, g), may be the one-dimensional vector represents the pupil function P ₂ (f, g):

P ₂ =(P ₂ (f ₁ ,g ₁ )P ₂ (f ₂ ,g ₁ )...P ₂ (f _M ,g ₁ )P ₂ (f ₁ ,g ₂ )...P ₂ (f _M ,g _M ))...(19)

If there are N point sources on the effective light source, the two-dimensional P operator 408 can be defined as follows:

Using ∣Φ' _2D and P _2D , the two-dimensional light intensity distribution I(x, y) formed on the wafer surface can be calculated by:

In equation (21), the singular value decomposition of P _2D yields the following equation:

In this way, even when calculating a two-dimensional spatial image (light intensity distribution), the elements of the P operator 408 are less than the elements of the TCC, and the P operator 408 does not require complicated calculations. This makes it possible to calculate a spatial image 409 as a light intensity distribution formed on the surface of the wafer in a relatively short period of time.

A two-dimensional vector group of light components diffracted by the mask pattern can be represented by:

Referring to the formula (23), Ψ _2D is a matrix of M columns × M rows, which includes M ² elements. According to the predetermined rule introduced herein, the operator (stacking operator) Y converts the M column x M row matrix into 1 column × M ² rows (i.e., elements rearranged Ψ _2D ). By introducing the operator Y , the vector ∣Φ' _{2D of the} two-dimensional diffracted light distribution is represented by the following equation:

∣Φ' _2D 〉= Y [Ψ _2D ] ^T ...(24)

Let (f ₁ , g ₁ ) be the coordinate of the first point source on the effective light source, and the output light from the first point source corresponds to the movement of the pupil of the projection optical system. The pupil function P ₁ (f, g) acting on the diffracted light is represented by P(f + f ₁ , g + g ₁ ). Therefore, the pupil function P ₁ (f, g) can be expressed by the following formula:

Similarly, let (f ₂ , g ₂ ) be the coordinate of the second light source on the effective light source, and denote the pupil function of the light emitted from the second point source with P(f+f ₂ , g+g ₂ ) P ₂ (f, g). Like the pupil function P ₁ (f, g), the pupil function P ₂ (f, g) can be expressed by:

Assume that there are N point sources on the effective light source. Using the stacking operator Y , the two-dimensional P operator 408 can be represented by:

When the spatial image formed on the surface of the wafer as the light intensity distribution is calculated by the equations (24) and (27), only the equation (21) or (22) is used.

When calculating TCC, you only need to use the following formula:

As indicated in the equations (20) and (27), the pupil of the projection optical system is moved according to the P operator 408 to form a point source in the column direction in the above description. However, the aperture of the projection optical system is moved according to the P operator 408 as indicated by the following equation to form a point source in the column direction:

P _2D =(Y[P ' ₁ ] ^T Y[P ' ₂ ] ^T ... Y[P ' _N ] ^T ) (29)

Can produce substantially the same effect. Therefore, even if the P operator 408 is represented by the equation (29), only the description of the orthogonal function system needs to be adjusted accordingly.

3 is a flow chart for explaining in detail a method of calculating a spatial image 409 by the spatial image calculation program 411. It is to be noted that the spatial image calculation program 411 is installed by the storage medium 70 connected to the media interface 60 and stored in the storage unit 40 via the control unit 20. And, the spatial image calculation program 411 is activated in response to the user's initial command input via the input unit 50, and is executed by the control unit 20.

In step S1002, the control unit 20 determines a spatial image calculation information piece, which includes effective light source information 402, NA information 403, λ information 404, aberration information 405, polarization information 406, photoresist information 407, and mask data 410. . More specifically, the user inputs (selects) the effective light source information of "quadrupole illumination", the NA information of "0.73", the λ information of "248 nm", and the aberration of "no aberration" to the processing device 1 via the input unit 50. Information, "non-polarized" polarized information, "don't consider" photoresist information, and "contact window" mask data. Next, the control unit 20 displays the (selected) spatial image calculation information input by the user on the display unit 30, and determines them. This embodiment exemplifies a case where the spatial image calculation information piece input (selected) by the user is stored in the storage unit 40. However, the user can input spatial image calculation information that is not stored in the storage unit 40.

In step S1004, the control unit 20 calculates the P operator 408. More specifically, the control unit 20 receives the (selected) spatial image calculation information input by the user from the storage unit 40. Based on the spatial image computing information, the control unit 20 calculates the P operator 408, for example, by equation (20) or (27). And, the control unit 20 stores the calculated P operator 408 in the storage unit 40.

In step S1006, the control unit 20 calculates the spatial image 409. More specifically, the control unit 20 calculates the spatial image 409 by, for example, the equation (21) or (22) using the P operator 408 and the (selected) spatial image calculation information input by the user. And, the control unit 20 displays the spatial image 409 on the display unit and stores it in the storage unit 40.

In this manner, the spatial image 409 can be calculated using the P operator 408 by the method of computing the spatial image 409 of the spatial image calculation program 411. In other words, the method of calculating the spatial image 409 by the spatial image calculation program 411 can calculate the TCC necessary for the spatial image 409 without calculating the SOCS. This allows the overall calculation to be simplified, thus reducing the time required to calculate the spatial image 409.

The calculation result of the spatial image 409 obtained by the spatial image calculation program 411 is analyzed as needed. Analysis of the spatial image includes, for example, NILS (normalized intensity log slope), contrast, out-of-focus characteristics (DOF characteristics), and the matching of the spatial image to the pattern data 401. The effect of the spatial image 409 on the photoresist can also be confirmed. Those skilled in the art can employ any known spatial image analysis.

The method of calculating a spatial image via the spatial image calculation program 411 can be applied to various forms of the model as the base RET.

The effect of the method of computing the spatial image 409 by the spatial image calculation program 411, the application of the calculation method to the model-based RET, and the like will be described in detail in the following embodiments.

<First Embodiment>

The effect of the method of calculating the spatial image 409 by the spatial image calculation program 411 will be explained in the first embodiment. In the first embodiment, a 64-bit Opteron is used. As the CPU, it includes the control unit 20 of the processing device 1, and uses about 10 billion bytes as the storage unit 40. Using MATLAB The spatial image calculation program 411 is generated in comparison with the time taken by the prior art (SOCS) to calculate the spatial image 409 (calculation time).

The first embodiment assumes that the exposure apparatus uses a projection optical system having an NA of 0.73 (corresponding to NA information 403) and exposure light having a wavelength of 248 nm (corresponding to λ information 404). In addition, it is assumed that the projection optical system has no aberration (corresponding to the aberration information 405), that the illumination light is not polarized (corresponding to the polarization information 406), and that the photoresist applied to the wafer is not considered (corresponding to the photoresist information) 407). Assume that a four-pole illumination effective source is used, as shown in Figure 4A. It is assumed that the pattern material (target pattern) includes two contact window patterns. Further, it is assumed that the diameter of each contact window pattern is 120 nm, and the centers of the respective contact window patterns are assumed to be (-120 nm, 0 nm) and (120 nm, 0 nm). Under this assumption, the mask data 410 is as shown in FIG. 4B. Further, it is assumed that the number of divisions of the pupil of the projection optical system in the normal state is 31, and the number of divisions of the pupil of the projection optical system when the Fourier transform is performed is assumed to be 1024.

Based on the spatial image calculation information described above, the control unit 20 calculates the P operator 408. At this time, the time taken to calculate the P operator 408 is equal to or less than 0.1 杪. And, the control unit 20 performs singular value decomposition of the P operator 408 (i.e., decomposes it into an eigenvalue and an eigenfunction). At this time, the time taken for the singular value decomposition of the P operator 408 is 0.4 seconds. When a complete spatial image is computed by adding all of the eigenfunctions, a spatial image 409 as shown in Figure 4C is obtained. The time taken to calculate the spatial image 409 is about 33.0 seconds. It is to be noted that the spatial image 409 shown in FIG. 4C is normalized assuming that its maximum value is 1.

Next, use SOCS to calculate the spatial image. The control unit 20 calculates the TCC based on the equation (2). At this time, the time taken to calculate the TCC is about 1152 seconds. And, the control unit 20 decomposes the TCC into an eigenvalue and an eigenfunction based on the equation (4) (first calculation step). At this time, the time taken to decompose the TCC into the eigenvalue and the eigenfunction is about 4.9 seconds. When a complete spatial image is calculated by adding all of the eigenfunctions (second calculation step), a spatial image as shown in Fig. 4D is obtained. The time taken to calculate the spatial image is approximately 1209 seconds. It is to be noted that the spatial image shown in Fig. 4D is normalized assuming that its maximum value is 1.

In this manner, the method of calculating the spatial image 409 by the spatial image calculation program 411 can calculate the spatial image in a shorter time period than the conventional SOCS. When the spatial image 409 shown in FIG. 4c is compared with the spatial image shown in FIG. 4D, they are equal to 1.0×10 ^-15 stages, and thus the correct simulation result is obtained.

Also, the spatial image calculation program 411 can calculate the TCC in a short period of time. As mentioned above, the SOCS takes about 1152 seconds to calculate the TCC. In contrast, after calculating the P operator 408 and based on equation (28), the control unit 20 calculates the TCC only for about 0.9 seconds.

<Second embodiment>

In the second embodiment, a method of calculating the spatial image 409 when the aberration of the projection optical system is considered or when the illumination light is polarized will be described. The method of calculating the spatial image 409 when the effective light source has a light intensity variation (the light intensity of the light-emitting portion is not uniform) or when the diffraction rate of the diffracted light by the mask pattern is changed will also be described in the second embodiment.

When considering the aberration of the projection optical system, it is only necessary to include aberrations in the pupil function and calculate the P operator 408 using equation (27). In this case, each element of the P operator 408 includes a conjugate element corresponding to the aberration of the projection optical system. Whereby the aberration of the projection optical system may include a P based on the formula (27) of _'i in.

It is assumed that the spatial image calculation information other than the aberration information 405 is the same as that of the first embodiment. The aberration of 50 mλ is substituted into the seventh item of the Fringe Zernike polynomial (lower coma aberration) as the aberration information 405. 5 shows the result of calculating the spatial image 409 using the P operator 408 for the mask data 410 shown in FIG. 4B according to the spatial image calculation program 411. Referring to Figure 5, the two contact windows that visualize the aerial image have different sizes, i.e., the left contact window pattern exhibits a larger spatial image element. This is because the low-order comet aberration is set as the aberration of the projection optical system.

Since the out-of-focus is a type of wavefront aberration, it can be included in the method of calculating the spatial image 409 by the spatial image calculation program 411. Assuming that the photoresist applied to the wafer is a parallel plate, the visible photoresist produces a circular aberration. Therefore, the photoresist-related aberration can be included in the method of calculating the spatial image 409 by the spatial image calculation program 411.

When the illumination light is polarized, it is only necessary to express the polarization three-dimensionally by making the σ of the effective light source corresponding to the NA of the projection optical system 1 . More specifically, the pupil function only needs to be multiplied by the polarization related factor. The factors related to polarization include factors that produce the effect of maintaining x-polarized light for x-polarization, factors that produce the effect of converting x-polarized light into y-polarized light, and generation of x-polarized light into z-polarization. a factor of the effect of light, a factor that produces the effect of converting y-polarized light into x-polarized light, a factor that produces the effect of maintaining y-polarized light for y-polarization, and a generation of y-polarized light for z-polarization The factor of the effect of light. Thus three P operators for x polarization, y polarization, and z polarization are obtained.

The light intensity distribution I(x, y) formed on the surface of the wafer can be calculated by the following formula:

Wherein P _x , P _y and P _z are P operators for x polarization, y polarization, and z polarization, respectively.

It is assumed that the spatial image calculation information pieces other than the polarization information 406 are the same as the first embodiment. All point sources are set to be polarized in the x direction as polarization information 406. 6 shows the results of calculating a spatial image using the P operators P _x , P _{y ,} and P _z for x polarization, y polarization, and z polarization, respectively, according to the spatial image calculation program 411. When comparing FIG. 6 with FIG. 4C, the spatial image 409 when the illumination light is polarized is blurred than the spatial image when the illumination light is not polarized.

The P operator is defined by:

Where P _pol is a P operator, which includes a polarization effect. Since P _pol has fewer elements than TCC, P _pol is used to calculate spatial image 409 in a shorter time period than SOCS.

This is an important conclusion. That is, a P operator is defined by a matrix, but a complex P operator can be defined by different matrices according to the present invention. For example, in the second embodiment, a P operator P _pol is defined by considering polarization, but three P operators can be defined for separately polarized light components. A plurality of P operators can also be defined by dividing the effective light source into a plurality of regions.

If the effective light source has a variable light intensity (the light intensity of the light-emitting portion is not uniform), it is only necessary to include the intensity of each point source in the P operator. For example, when the i-th point source is S _i , the P operator is defined by:

As the micropatterning of the mask pattern progresses, the diffracted light distribution at normal incidence is often different from the diffracted light at oblique incidence (ie, the diffraction rate often changes). In this case, it is only necessary to rewrite equation (27) as follows:

It is to be noted that P'' _i in the equation (33) includes a diffraction rate when light emitted from the i-th point source obliquely enters the surface of the wafer.

<Third embodiment>

The third embodiment will explain a case where a method of calculating a spatial image by applying the spatial image calculation program 411 to the model RET is explained. A simple method of OPC (optical proximity correction) is known as RET.

It is assumed that the spatial image calculation information other than the mask data 410 is the same as the first embodiment. In the third embodiment, five bar systems each having a width of 120 nm and a length of 840 nm as shown in FIG. 7A are assumed as the mask data 410. FIG. 7B shows the spatial image 409 calculated by the spatial image calculation program 411 in this case. When comparing FIGS. 7A and 7B, the mask data 410 is different from the spatial image 409 calculated by the spatial image calculation program 411. To solve this problem, the mask data 410 is changed based on the OPC so that the spatial image 409 (that is, the pattern transferred by the exposure) calculated by the spatial image calculation program 411 becomes the approximate pattern data 401.

In order to determine the optical mask data 410 in the OPC, it is necessary to repeat the loop for calculating the spatial image 409 by changing the mask data 410 until the difference between the spatial image 409 and the pattern data 401 is sufficiently reduced. For this reason, when the spatial image 409 is calculated for a long time, the optical mask data 410 is determined for a long time. However, since the spatial image calculation program 411 can calculate the spatial image 409 in a short period of time, it is suitable for OPC.

More specifically, in order to determine the optical mask data 410, the control unit 20 repeats the method of calculating the spatial image 409 by the spatial image calculation program 411 for the above five bars, thereby changing the mask data 410. In this operation, a final mask data 410 is obtained, wherein the leftmost and rightmost rods each have a width of 134 nm and a length of 968 nm, and the left and right second rods each have a width of 127 nm and a length of 930 nm, and a center rod. It has a width of 120 nm and a length of 929 nm. FIG. 7C shows a spatial image 409 calculated by the spatial image calculation program 411 using the mask data 410. When comparing FIGS. 7B and 7C, the spatial image 409 shown in FIG. 7C is more similar to the pattern material 401 than the spatial image 409 shown in FIG. 7B.

In this manner, the method of computing the spatial image 409 by the spatial image calculation program 411 to the OPC is applied, making it possible to generate the mask pattern 410 in a shorter period of time.

<Fourth embodiment>

In the fourth embodiment, a method of calculating the spatial image 409 in a shorter time period than the method of calculating the spatial image 409 by the spatial image calculation program 411 in the previous embodiment will be described.

When the two-dimensional space image 409 is calculated, as described above, the P operator 408 can be represented by the equation (27). Let L be the number of pupil divisions, and N be the number of point sources, and define the P operator by a matrix of N columns and (2L) ² rows. Since the columns of the P operators are independent of each other, the order of the P operators is N. In other words, the singular value decomposition of the P operator produces an N eigenvalue and an N eigenfunction. Therefore, the N eigenvalue and the N eigenfunction are necessary for calculating the complete spatial image 409. However, in practice, as explained below, it is not necessary to use the N eigenvalue and the N eigenfunction.

It is assumed that the spatial image calculation information piece other than the mask data 410 is the same as the first embodiment. In the fourth embodiment, five bar systems each having a width of 120 nm and a length of 840 nm as shown in FIG. 7A are assumed as the mask data 410.

The effective source shown in Figure 4A has 92 point sources for numerical calculations. This represents 92 eigenvalues and 92 eigenfunctions. The eigenfunctions corresponding to the eigenvalues are rearranged in descending order of the eigenvalue squared.

Figure 8A is a plot of the eigenvalue squared, which is normalized assuming that the largest eigenvalue is squared to one. As mentioned above, there are 92 eigenvalues. Let i be the eigenvalue, that is, the i-th eigenvalue, and if i is 10 or more, the square of the i-th eigenvalue is 0.01 or less, as shown in FIG. 8A. And, if i is 49 or more, the square of the i-th eigenvalue is 0.001 or less. In this way, as the eigenvalue i increases, the square of the ith eigenvalue decreases significantly.

Let E be the sum of the squares of all eigenvalues, and E _i be the sum of the squares of the first to ith eigenvalues here. When E _i /E=1, a complete spatial image 409 can be calculated. When the light intensity is set in the full-space image 409 such that the line width of the center rod in the y=0 portion is 120 nm, the line width of the leftmost rod is 98.44 nm.

As the eigenvalue i increases, the square of the eigenvalue decreases significantly, and as the eigenvalue i increases, the special frequency of the eigenfunction increases. According to this principle, as the number of eigenvalues i increases, the influence of the i-th eigenvalue used to form the spatial image decreases. Figure 8B shows the difference between a full-space image and an approximate spatial image (i.e., a spatial image calculated from some eigenvalues and eigenfunctions). In Fig. 8B, the abscissa indicates the eigenvalue i, and the ordinate indicates the line width of the leftmost stick when the spatial image is calculated using the first to ith eigenvectors and the eigenvalue. Referring to Fig. 8B, when E _i /E ₌ 0.96 or more (i.e., the eigenvalue i is 14 or more), the difference between the full-space image and the approximate spatial image is 0.1 nm or less. Therefore, instead of using 92 eigenvalues and 92 eigenfunctions but using 14 eigenvalues and 14 eigenfunctions, a spatial image that is almost equal to a full-space image can be calculated. This makes it possible to shorten the time taken to calculate about 85% of the spatial image.

The accuracy required for spatial imaging varies depending on the target of the assessment. By examining various cases, the inventors of the present invention found that when E _i /E is 0.96 or more, there is no problem in terms of practical application. Further, the inventors of the present invention found that when E _i /E is 0.96 or more, almost all evaluation targets have no problem.

In this manner, E _i /E is adjusted according to the evaluation target in the method of calculating the spatial image 409 by the spatial image calculation program 411, and the spatial image 409 can be calculated in a shorter time period than the previous embodiment.

Another method of computing a spatial image 409 in a shorter time period than in the previous embodiment includes a method of compressing the P operator 408. For example, consider one-dimensional imaging. If the components of the jth row of the P operator 408 are both 0, the component of the jth row is not necessary at all. Next, by deleting each row of the P operator 408 whose components are 0, the P operator 408 can be compressed as shown in the following equation:

Referring to the equation (34), the P operator 408 that compresses two columns and seven rows becomes two columns and four rows.

Similarly, the P operator 408 can be compressed even in two-dimensional imaging. More specifically, the P operator 408 can be compressed by deleting each row of the P operator 408 that has a component of zero. The use of the compressed P operator 408 thereby enables singular value decomposition in a shorter time period than in the prior embodiments. This makes it possible to calculate the spatial image 409 in a shorter period of time than in the previous embodiment.

The case where the P operator 408 is compressed will now be described in detail. Assume that an effective source of four-pole illumination is used and that the effective source includes 712 point sources, as shown in Figure 9A. FIG. 9B shows the P operator 408 (ie, uncompressed) that is generally calculated based on the spatial image calculation program 411. The P operator 408 shown in FIG. 9B is a matrix of 712 columns and 16129 rows, in which the white portion corresponds to 1, and the black portion corresponds to 0. Figure 9C shows P operator 408 compressed by a predetermined method. The P operator 408 shown in Figure 9C is a matrix of 712 columns and 10641 rows, where the white portion corresponds to 1, and the black portion corresponds to zero.

The singular value decomposition of the P operator 408 shown in Figure 9B takes about 34.0 seconds. In contrast, the singular value decomposition of the P operator 408 shown in Figure 9C takes about 24.3 seconds. In this manner, the compression P operator 408 improves the speed at which the singular value decomposition of the P operator 408 is performed.

<Fifth Embodiment>

In the fifth embodiment, a method of using the model of the P operator 408 as the base RET to generate the mask data 410, particularly the method of calculating the spatial image 409 by the spatial image calculation program 411 will be described. This method produces mask material 410 by inserting (auxiliary) patterns into the pattern to be transferred by exposure.

Figure 10 is a schematic block diagram showing the configuration of a processing apparatus 1 according to a fifth embodiment of the present invention. The processing apparatus 1 shown in FIG. 10 basically has the same configuration as the processing apparatus 1 shown in FIG. 1, but the storage unit 40 additionally stores a mask function 412, a P map 413, and a mask generating program 414. Hereinafter, the effective light source information 402, NA information 403, λ information 404, aberration information 405, polarization information 406, photoresist information 407, mask data 410, and mask function 412 will be collectively referred to as P image calculation information.

The mask function 412 is a parameter for the P map 413 (which will be described below), and is the pattern material 401 of its own or obtained by converting the pattern material 401 according to a predetermined rule.

The P map 413 is a partial homomorphic map obtained by multiplying the eigenfunction of the P operator 408 by the diffracted light distribution and the Fourier transform or adding the resulting product.

The difference between the method of calculating the P map 413 and the calculation of the spatial image 409 will now be described. The method of computing the spatial image 409 is such that the eigenfunction of the P operator 408 is multiplied by the diffracted light distribution on the mask data 410, the product resulting from the Fourier transform, and the square of the absolute value of the Fourier transform. The square of the absolute value is then multiplied by the square of their corresponding eigenvalues and the resulting product is added. The spatial image 409 is calculated in this operation. Conversely, by multiplying the eigenfunction of the P operator 408 by the diffracted light distribution on the mask data 410, the product of the Fourier transform, multiplying the Fourier transform by their corresponding eigenvalues, and adding the resulting product To calculate the P image 413. Therefore, the spatial image 409 is always a positive value, but the P map 413 is not necessarily a positive value. The P map 413 is intended to mean an image (function) that affects each other when a plurality of pattern elements are inserted on the object plane of the projection optical system.

The mask generation program 414 is based on the P image 413 for generating a mask data 410.

A method of inserting an auxiliary pattern to generate a mask data 410 by mask generation of a program 414 will be described below.

The fifth embodiment assumes that the exposure apparatus uses a projection optical system having an NA of 0.73 (corresponding to NA information 403) and a case where the wavelength of exposure light is 248 nm (corresponding to λ information 404). Furthermore, it is assumed that the projection optical system has no aberration (corresponding to the aberration information 405), that the illumination light is non-polarized (corresponding to the polarization information 406), and that the photoresist applied to the wafer is not considered (corresponding to the photoresist information) 407). It is assumed that the effective light source (corresponding to the effective light source information 402) uses quadrupole illumination, as shown in Figure 11A. It is assumed that the pattern material (target pattern) 401 is a contact window pattern having a side length of 120 nm, as shown in FIG. 11B.

It is also assumed that the fifth embodiment has a dark field of view with a clear aperture. In this case, the pattern is formed on the photoresist portion irradiated with the light for exposure.

Since the various values can be set to the wavelength λ of the exposure light and the numerical aperture NA of the projection optical system in the exposure apparatus, it is preferable to normalize the size of the mask pattern by (λ/NA). For example, if λ = 248 nm and NA = 0.73, the pattern having a size of 100 nm is normalized to 0.29 by the above method. This is usually referred to as the k1 conversion.

The isolated contact window pattern having a diameter of 120 nm has a k1 conversion value of 0.35. If the k1 conversion value is 0.5 or less, a sinusoidal space image is obtained. To best use the sinusoidal characteristics, an auxiliary pattern is conventionally inserted at a half cycle of the diameter of the isolated contact window pattern. For example, if the center of the contact window pattern as the desired pattern is located at (0, 0), an auxiliary pattern is inserted at eight positions, namely (±240, 0), (0, ±240), (240, ± 240) and (-240, ±240).

In the mask generation program 414, the mask function 412 is first set to the target pattern itself, that is, the diameter of the isolated contact window pattern is 120 nm.

As explained in the fourth embodiment, as the eigenvalue of the P operator 408 increases, the effect of the eigenfunction of the P operator 408 used to form the spatial image 409 increases. To achieve this state, the eigenvalues of the P operator 408 are rearranged in descending order of the eigenvalue squared. Hereinafter, the eigenfunction corresponding to the i-th eigenvalue rearranged in this manner is referred to as the i-th eigenfunction.

The first eigenfunction of P operator 408 has the greatest impact on forming spatial image 409. For this reason, only the first eigenfunction of the P operator 408 needs to be considered. The first eigenfunction of P operator 408 is multiplied by the diffracted light distribution of mask function 412 and the resulting product is Fourier transformed. Figure 11C shows the P image 413 calculated in this manner.

In Fig. 11C, the values in the AR1 to AR8 regions surrounded by white dotted lines are quite large. In other words, the light component diffracted via the AR1 to AR8 regions interferes with the light component that is diffracted via the target pattern, thereby improving the image intensity. Therefore, when an open pattern is inserted in the AR1 to AR8 area surrounded by a white dotted line, the image intensity at the position (0, 0) increases.

The auxiliary patterns HP1 to HP8 are inserted into the AR1 to AR8 areas surrounded by white dotted lines as shown in Fig. 11D. As described above, the original intention is to transfer the isolated contact window pattern centered at (0, 0) onto the wafer surface by exposure. When the P map 413 is analyzed, the position of the P map 413 having a peak is (0, 0). The auxiliary patterns HP1 to HP8 are set such that the center of the main pattern SP having the same size as the pattern material 401 becomes (0, 0). A mask is then fabricated as the mask material 410 by using the mask pattern shown in FIG. 11D. In this operation, the light component diffracted by the auxiliary patterns HP1 to HP8 acts on the light component diffracted by the main pattern SP. This allows the transferable isolated contact window pattern to be a target pattern with high accuracy, thus improving analytical performance.

Figure 12 shows the imaging performance of a mask without an auxiliary pattern, the imaging representation of a mask inserted according to the prior art, and the masking of the auxiliary pattern (i.e., by the mask generating program 414) according to the fifth embodiment. The comparison of the imaging performance of the hood. In Fig. 12, the abscissa indicates the amount of defocus and the ordinate indicates the diameter (CD) of the contact window pattern. The imaging performance of each mask is evaluated based on the change in diameter (CD) of the isolated contact window relative to the change in out-of-focus. The size of each auxiliary pattern in the prior art is 90 nm x 90 nm. The size of each auxiliary pattern in the fifth embodiment will be described below.

Referring to Figure 12, the imaging representation of a mask without an auxiliary pattern is compared to the imaging representation of a mask inserted with an auxiliary pattern according to the prior art. In this case, the change in the radius of the contact window pattern of the mask inserted into the auxiliary pattern according to the prior art with respect to the mask out of focus change is significantly smaller than that of the mask without the auxiliary pattern. In other words, a mask that inserts an auxiliary pattern according to the prior art exhibits a better imaging feature than a mask with no auxiliary pattern.

Similarly, the imaging performance of the mask in which the auxiliary pattern is inserted according to the prior art is compared with the imaging performance of the mask in which the auxiliary pattern is inserted according to the fifth embodiment. Referring to Fig. 12, the mask in which the auxiliary pattern is inserted according to the fifth embodiment exhibits an imaging feature superior to the mask in which the auxiliary pattern is inserted according to the prior art.

The P map 413 shown in Fig. 11C will now be described in detail. On the P map 413 shown in Fig. 11c, a first position having a peak value higher than a predetermined threshold value is detected. The position with the peak indicates the value obtained by the differential P map 413 with respect to the 0 position. The first position is a vector that includes distance and direction information. In the fifth embodiment, the first position is eight positions, namely (±285, 0), (0, ±285), (±320,320), and (±320, -320). It is to be noted that the P map 413 of Fig. 11C is assumed to have a maximum value of 1 and normalized, and a threshold value of 0.03. When the first position is calculated, the auxiliary pattern is inserted as faithfully as possible on the light intensity distribution of the P image 413. In the fifth embodiment, an auxiliary pattern of a rotationally symmetric rectangle each having a size of 70 nm × 120 nm is inserted (arranged) at eight positions.

It is difficult to calculate the peak position by numerical calculation. Using the fact that the peak position is nearly identical to the position of the center of gravity, the center of gravity of the region that appears above the value of the predetermined threshold on the P map 413 can be calculated and set to the first position.

For example, FIG. 11E shows that on the P map 413 shown in FIG. 11C, each region that sets a value of a threshold value equal to or higher than 0.03 is set to 1, and a threshold of less than 0.03 is set by setting. The area obtained by the value of each value is 0. In FIG. 11E, the region SR corresponding to the main pattern SP serves as an isolated contact window pattern (desired pattern). The areas HR1 to HR8 correspond to areas (i.e., areas AR1 to AR8) to insert (configure) an auxiliary pattern. Therefore, it is only necessary to set the auxiliary pattern by calculating the centers of gravity of the areas HR1 to HR8.

<Sixth embodiment>

In the sixth embodiment, a method of generating the mask data 410 when the pattern material (target material) 401 is a pattern formed by the n contact window pattern will be described.

As described in the fifth embodiment, the use of the P map 413 to create the mask data 410 improves the imaging performance of the mask with the isolated contact window pattern. Likewise, the use of P-map 413 to create mask data 410 can also improve the imaging performance of a mask having a pattern formed by the n-contact window pattern.

It is assumed that the P-picture calculation information piece other than the mask function 412 is the same as the fifth embodiment. It is assumed that the pattern material (target pattern) 401 is a pattern including three 120 nm square contact window patterns as shown in FIG. 13A. The centers of the three contact windows are (0,0), (320,320) and (640,-350). The mask function 412 is the target pattern itself, that is, as in the fifth embodiment, the pattern includes three contact window patterns each having a diameter of 120 nm.

The first eigenfunction of P operator 408 has the greatest contribution to forming spatial image 409. For this reason, only the first eigenfunction of the P operator 408 is considered. The first eigenfunction of the P operator 408 is multiplied by the diffracted light distribution of the mask function 412 and the resulting product is Fourier transformed. Figure 13B shows the P image 413 calculated in this way.

In Fig. 13B, the area surrounded by the respective white dotted lines appears to be equal to or larger than a specific threshold (0.025 in the fifth embodiment) and corresponds to the value of the peak position. It is only necessary to insert (configure) the auxiliary pattern in the area surrounded by the white dotted line shown in FIG. 13B.

Next, how to determine the main pattern corresponding to the pattern material 401 will be explained. First, the center of the pattern data is seen at the position (0, 0). When the P map 413 is analyzed, its peak is at a position shifted from (0, 0) (δx, δy). When the position of the 120 nm square main pattern center is at (0, 0), it is transferred by exposure when moving by (δx, δy) due to the optical proximity effect.

By arranging the center of the main pattern at the position (-δx, -δy), the unmoved movement can be canceled. Similarly, when the main patterns are contact windows and their centers are located at (320, 320) and (640, -350), they are similarly inserted (configured) to a position different from the pattern material 401.

The analysis of the P map 413 also makes it possible to predict the deformation angle of the main pattern. Therefore, the shape of the main pattern can be determined based on the deformation thereof.

After the main pattern is determined as the pattern represented by the pattern material 401 itself based on the P map 413, the positional movement and shape of the main pattern can be corrected by using the OPC.

Depending on the configuration of the contact window pattern, the auxiliary patterns are often configured too close to each other. In this case, it is only necessary to insert (configure) one pattern to approach the adjacent auxiliary pattern. If an auxiliary pattern is close to the desired pattern, it should be removed.

<Seventh embodiment>

The application target of the mask generation program 414 is not particularly limited to a mask having a square contact window pattern, and it can be applied to a mask having a rectangular contact window pattern or a line pattern. The seventh embodiment will explain the case where the mask generation program 414 is used to generate the mask material 410 having an isolated line pattern.

It is assumed that the P-picture calculation information pieces other than the effective light source information 402 and the mask function 412 are the same as the fifth embodiment. It is assumed that the effective light source (corresponding to the effective light source information 402) uses dipole illumination as shown in Figure 14A. It is assumed that the pattern data (target pattern) 401 is an isolated line pattern having a width of 120 nm.

The seventh embodiment also assumes that a so-called clear field has an opaque feature in which a pattern is formed on a photoresist portion irradiated with light for exposure, and a value equal to or smaller than a specific threshold value appears.

First, the mask function 412 is set to the target pattern itself, that is, an isolated line pattern of 120 nm. In general, when the transfer line pattern is exposed by exposure, only the unremoved photoresist is left in the line portion. Thus, the mask function 412 indicates that the mask exhibits a background transmittance of 100% and that the mask has a light-shielding portion formed by a line pattern of 120 nm isolation.

Fig. 14B shows a P map 413 calculated by the above P image calculation information. The imaging performance of the mask is improved when the auxiliary pattern is inserted (configured) into an area where each display value is less than the predetermined threshold value and corresponds to the peak position of the P map 413 shown in FIG. 14B.

The P map 413 shown in Fig. 14B has a peak at a position of about 290 nm from the center of the isolated line pattern. The imaging performance is improved using a mask in which the auxiliary pattern is disposed at a position of about 290 nm from the center of the isolated line pattern, as shown in Fig. 14C. In Fig. 14C, reference symbol d indicates the distance from the center of the isolated line pattern, which is 290 nm in the seventh embodiment.

Even if the auxiliary pattern is inserted (arranged) in the following manner, the mask material 410 having the mask of the isolated line pattern can be produced.

First, the P map 413 which is a dark field having a clear aperture is calculated to be set to PM ₁ (x, y). It is to be noted that the P map 413 is normalized assuming that the maximum value of PM ₁ (x, y) is 1. Next, a new P map 413 is calculated by setting PM ₂ (x, y) = 1 - PM ₁ (x, y). Inserting (arranging) an auxiliary pattern into a region each exhibiting a value less than a predetermined threshold and corresponding to a peak position (or a center of gravity position) on PM ₂ (x, y) calculated in this manner, thereby generating mask data 410. An auxiliary pattern for forming a bright field having opaque features can be inserted (configured) into regions each exhibiting a value greater than a predetermined threshold and corresponding to a peak position (or center of gravity position).

<Eighth Embodiment>

The mask function 412 will be described in detail in the eighth embodiment.

It is assumed that the P-image calculation information pieces are identical to the fifth embodiment. It is assumed that the pattern data (target pattern) 401 is a 120 nm square isolated contact window pattern.

15A and 15B show a P map 413 calculated by setting the mask function 412 as the target pattern itself. Fig. 15A shows the P map 413 itself. Fig. 15B shows an image obtained by setting a positive value of each position to 1, and setting a negative value of -1 at each position on the P map 413 shown in Fig. 15A.

Figures 15C and 15D show a P-map 413 calculated by setting the mask function 412 to a 60 nm square isolated contact window pattern. Figure 15C shows the P map 413 itself. Fig. 15D shows an image obtained by setting a positive value of each position to 1, and setting a negative value of -1 at each position on the P map 413 shown in Fig. 15C.

Figures 15E and 15F show a P-map 413 calculated by setting the mask function 412 to a 1 nm square isolated contact window pattern. Figure 15E shows the P image 413 itself. Fig. 15E shows an image obtained by setting a positive value of each position to 1, and setting a negative value of -1 at each position on the P map 413 shown in Fig. 15F.

When a relatively small pattern is set as the mask function 412, the auxiliary pattern is inserted (arranged) so that light is concentrated on the small pattern, resulting in an increase in exposure margin. However, as can be understood from FIGS. 15A to 15F, the mask shape is complicated in this case. Conversely, when a relatively large pattern is ordered as the mask function 412, the mask shape is simple. According to various cases tested by the inventors of the present invention, a size equal to or smaller than the size of the target pattern is set as the mask function 412.

To simplify the calculation of the P-map 413, the mask function 412 is only required to be set by approaching the contact window pattern (eg, a 1 nm contact window pattern) and a line-to-line pattern (eg, a pattern having a width of 1 nm). If a rectangular contact window is used, it is only necessary to set a line extending in the longitudinal direction (such as a pattern having a length equal to the length of the rectangular contact window pattern in the longitudinal direction and having a width of 1 nm) as the mask function 412.

For example, in the fifth embodiment, only a 1 nm isolated contact window pattern needs to be set as the mask function 412. In the sixth embodiment, only a pattern including three 1 nm contact window patterns is required as the mask function 412. In the seventh embodiment, it is only necessary to set a line pattern having a width of 1 nm as the mask function 412.

As described above, the desired mask function 412 is a pattern having a size equal to or smaller than the target pattern. Therefore, the reduction magnification can be reset from 0 (not included) to 1 (inclusive), and the product of the reduction magnification and the original size of the target pattern can be set as the mask function 412.

For example, to set the reduction magnification to 0.75, it is only necessary to set a 90 nm (120 nm × 0.75) isolated contact window pattern as the mask function 412 in the fifth embodiment. It is only necessary to set a line pattern having a width of 90 nm as the mask function 412 in the seventh embodiment. It is to be noted that each of the fifth to seventh embodiments exemplifies a case where the reduction magnification is set to 1.

Generally, it is difficult to analyze the line pattern and the rectangular pattern in the lateral direction, and thus the lateral resolution of the pattern is concerned. For this reason, the P map 413 can be calculated as the mask function 412 by setting the reduction magnification and the original size of the target pattern in the lateral direction.

<Ninth embodiment>

The insertion (configuration) of the auxiliary patterns in the ninth embodiment will be explained in the regions (positions) each having a negative value on the P map 413.

The P map 413 includes an area having a negative value. This indicates that the formation of the spatial image on the P map 413 is canceled in the area.

The effect of canceling the spatial image formation can be interpreted as inverting the light (ie, setting the light to be 180° out of phase). Therefore, by inserting (arranging) the auxiliary pattern to each region having a negative value on the P map 413 such that the light penetrating the desired pattern is 180° out of phase with the light penetrating the auxiliary pattern, the imaging performance of the mask can be improved.

It is assumed that the P-image calculation information piece is the same as the fifth embodiment. It is assumed that the pattern data (target pattern) 401 is an isolated contact window pattern having a diameter of 120 nm.

As explained in the fifth embodiment above, the P map 413 shown in Fig. 11C is calculated by the above P map calculation information. The imaging performance of the mask is improved when the auxiliary pattern inserted (configured) in phase with the desired pattern (0° out of phase) is in the areas AR1 to AR8 surrounded by the white dotted line in FIG. 11C. It is to be noted that the areas AR1 to AR12 surrounded by the white dotted line on the P map 413 shown in Fig. 11C have considerably large negative peaks as shown in Fig. 16A. On the P map 413 shown in Fig. 16A, the centers of the areas AR9 to AR12 surrounded by the white dotted line are located at four positions, namely (±225, 225) and (±225, -225). The mask data 410 shown in Fig. 16B is produced by inserting (arranging) the auxiliary patterns AP1 to AP4 into the areas AR9 to AR12 surrounded by the white dotted lines, which are 180 out of phase with the desired pattern. In FIG. 16B, the auxiliary patterns AP1 to AP4 are each 180° out of phase with the desired pattern, and each has a size of 90 nm×90 nm.

Figure 17 is a diagram showing the imaging performance of the mask according to the mask data 410 shown in Figure 11D (i.e., according to the fifth embodiment) and the mask of the mask data 410 shown in Figure 16B (i.e., according to A chart of the comparison result of the ninth embodiment). In Fig. 17, the abscissa indicates the amount of out-of-focus, and the ordinate indicates the diameter of the isolated contact window pattern (CD). The imaging performance of each mask was evaluated based on the change in diameter of the isolated contact window pattern (CD) relative to the out-of-focus change. Referring to Figure 17, a mask based on the mask data 410 shown in Figure 16B exhibits a better imaging performance than a mask based on the mask data 410 shown in Figure 11D.

In this manner, the mask imaging performance can be improved by inserting (arranging) an auxiliary pattern having a 180° out of phase with the desired pattern in a region having a negative value on the P map 413. Therefore, it is only necessary to insert an auxiliary pattern in phase with the desired pattern in each region that exhibits a value greater than the positive threshold and corresponds to the peak position, and inserts an auxiliary pattern that is 180° out of phase with the desired pattern to appear less than negative. The value of the threshold value and corresponds to each region of the peak position. In the ninth embodiment, the positive threshold is 0.03, and the negative threshold is -0.018.

<Tenth embodiment>

As has been explained in the fifth and ninth embodiments, mask imaging performance can be improved by generating mask data 410 based on P-map 413. However, when the auxiliary pattern is faithfully inserted (configured) to the P image 413, the shape of the mask is complicated. Existing mask manufacturing techniques can produce a mask based on the mask data 410 shown in Figure 11D and based on the mask data 410 shown in Figure 16B. Even so, it is very useful to reduce the load applied to the mask manufacturing.

In order to reduce the load applied to the mask fabrication, it is only necessary to insert an auxiliary pattern approximating the pattern to be transferred by exposure to a region exhibiting a value greater than a predetermined threshold and corresponding to a peak position on the P map 413. Since the P map 413 has the most obvious features at the specified position to insert (configure) the auxiliary pattern, the shape change of each auxiliary pattern has little effect on the mask imaging performance.

It is assumed that the P-image calculation information piece is identical to the fifth embodiment. It is assumed that the pattern data (target data) 401 is an isolated contact window pattern having a diameter of 120 nm.

As has been explained in the fifth embodiment, the regions appearing equal to or larger than the value of the positive threshold and corresponding to the peak position on the P map 413 calculated via the P map calculation information are located at eight positions, That is (±285,0), (0, ±285), (±320,320) and (±320,-320). An auxiliary pattern in phase with the pattern to be transferred by exposure is inserted at these eight positions. It is to be noted that each of the auxiliary patterns is assumed to be an isolated contact pattern as a desired pattern and has a size of 90 nm × 90 nm.

As explained in the ninth embodiment, at four positions, namely (±225, 225) and (±225, -225), the insertion is 180° with the light diffracted by the pattern to be transferred by exposure. Auxiliary pattern of out of phase. It is to be noted that each of the auxiliary patterns is assumed to be approximately an isolated contact pattern as a desired pattern to be transferred by exposure, and has a size of 90 nm × 90 nm.

Figure 18 shows the mask data 410 generated in this manner. In FIG. 18, the auxiliary patterns AP5 to AP12 are in phase with the pattern to be transferred by exposure, and are inserted (configured) to (±285, 0), (0, ±285), (±320, 320), and (±320, -320). The auxiliary patterns AP13 to AP16 are 180° out of phase with the pattern to be transferred by exposure, and are inserted into (±225, 225) and (±225, -225). Since the auxiliary patterns AP13 to AP16 each have a square shape (that is, approximate a desired pattern) on the mask based on the mask material 410 shown in FIG. 18, the mask can be manufactured based on the one shown in FIG. 16B. The mask of the mask data 410 is simple to manufacture.

Figure 19 is a view showing the imaging performance of the mask according to the mask data 410 shown in Figure 16B (i.e., according to the ninth embodiment) and the mask according to the mask data shown in Figure 18 (i.e., according to the A chart of the comparison results of the tenth embodiment). Referring to Fig. 19, the imaging performance of the mask based on the mask data 410 shown in Fig. 16B is slightly different from that of the mask based on the mask data 410 shown in Fig. 18. In this way, by inserting (arranging) an auxiliary pattern approximating the pattern to be transferred by exposure to each region exhibiting a value greater than a predetermined threshold and corresponding to the peak position, the application to the mask manufacturing can be reduced. load. Furthermore, masks made in this manner can improve imaging performance as compared to masks made according to the prior art. Each of the auxiliary patterns is not particularly limited to almost the same as the desired pattern, and any form may be employed as long as it promotes the manufacture of the mask.

When each of the auxiliary patterns is nearly to be transferred by the exposure, it preferably has a size of about 75% of the contact pattern to be transferred by exposure. This size does not represent the area but is the length of one side of the pattern. For example, when one side of a square pattern of 120 nm is formed on the mask to transfer a contact window of 120 nm by exposure, the length of one side of each auxiliary pattern need only be about 90 nm. Since the P map 413 appropriately indicates the position of the insertion (configuration) of the auxiliary pattern, the insertion (configuration) of the auxiliary pattern gives a considerable improvement in the resolution. Therefore, it is not necessary to fix the size of each auxiliary pattern to 75% of the size of the contact window pattern to be transferred by exposure. According to various tests by the inventors of the present invention, even if the size of each auxiliary pattern is 50% to 85% of the size of the contact window pattern to be transferred by exposure, a sufficient effect of inserting the auxiliary pattern can be obtained.

If the contact window pattern has a rectangular shape, it is only necessary to insert (configure) a rectangular auxiliary pattern. The length of the short side of these auxiliary patterns need only be 50% to 80% of the length of the short side of the contact window pattern to be transferred by exposure.

If the pattern to be transferred by exposure is a line pattern, only the linear auxiliary pattern needs to be inserted. Since the linear pattern is easy to be resolved, the width of each auxiliary pattern is preferably from 35% to 70% of the width of the line pattern to be transferred by exposure.

<Eleventh Embodiment>

Multiple exposure using the P map 413 will be explained in the eleventh embodiment. In the broad sense, multiple exposure is considered to be a micropattern exposure method. Generalized multiple exposures include narrow multiple exposures and multiple exposures. In the narrow multiple exposure, the latent image pattern is added without the need for a development process. For example, in a representative double exposure, the mask pattern is divided into two types, a dense pattern and a sparse pattern, thereby exhibiting double exposure. In another double exposure, the line pattern is divided into patterns in the longitudinal and lateral directions, and they are independently transferred by exposure, thereby forming a desired line pattern. Conversely, in a plurality of exposures, a latent image pattern is added by a developing process. These exposure architectures are methods for reducing the k1 factor, and will be referred to hereinafter simply as "multiple exposures", which term includes narrow multiple exposures and multiple exposures.

As previously mentioned, the P-map 413 includes regions of negative values and has a function of canceling imaging (ie, forming a spatial image).

It is assumed that the P-image calculation information piece is identical to the fifth embodiment. Figure 20 shows the out-of-focus feature when inserting (arranging) an auxiliary pattern in phase with a desired pattern to be transferred by exposure to a region having a positive value, and when inserting an auxiliary pattern in phase with the desired pattern The P image calculates the out-of-focus feature when the position on the P map 413 calculated by the information piece has a negative value. Figure 20 also shows the out-of-focus feature when there is no auxiliary pattern. In Fig. 20, the abscissa indicates the amount of defocus, and the ordinate indicates the diameter (CD) of the contact window pattern.

Referring to Fig. 20, the out-of-focus feature when the auxiliary pattern is inserted (arranged) with a positive position is better than the out-of-focus feature when the auxiliary image is not provided on the P map 413. However, the out-of-focus feature when inserting (arranging) the auxiliary pattern at a negative position is inferior to that of the P-image 413 when there is no auxiliary pattern. In this manner, FIG. 20 shows that it is not always advantageous to increase the number of auxiliary patterns disposed around the pattern to be transferred by exposure, which is different from the conventional concept.

A position with a negative value on the P map 413 indicates a disabled pitch. A position vector having a negative value on the P map 413 depends on the distance and direction. In this case, the four vectors, (±225, 225) and (±225, -225), indicate the disabled spacing. These vectors each point in the direction from the origin to the region of the homology that appears equal to or less than the threshold value on the P map 413.

When the pattern data 401 is divided to avoid disabling the pitch (assuming a vector indicating the pitch is disabled as a reference vector), the final pattern material 401 without any prohibited pitch can be generated.

A method of generating the pattern material 401 without any prohibited pitch by the mask generating program 414 will be described in detail with reference to FIG. It is assumed that the user inputs the P image calculation information piece via the input unit 50 in advance and the P image calculation information piece is stored in the storage unit 40. And, assume that via the control unit 20, the mask generation program 414 is to be installed by the storage medium 70 connected to the media interface 60 and stored in the storage unit 40. The mask generation program 414 is activated in response to a start command input by the user via the input unit 50, and is executed by the control unit 20.

In step S1102, the control unit 20 calculates the P map 413 based on the P map calculation information. It is to be noted that the mask function 412 is not set based on the overall pattern data (target pattern) 401 but based on one of the elements. More specifically, the mask function 412 is set by performing a predetermined method for one element of the target pattern (eg, by amplifying the magnification).

In step S1104, the control unit 20 specifies the reference vector representing the disabled pitch from the P map 413 calculated in step S1102. More specifically, the reference vector is specified by capturing the number of vectors from the origin to the appearance of a region equal to or smaller than the threshold value on the P map 413 and corresponding to the region of the negative peak on the P map 413.

In step S1106, the control unit 20 sets the initial value of the reference number i of the pattern data 401 (generated in the following steps) to "1". Thereafter, the pattern material having the reference number i is regarded as the i-th pattern material.

In step S1108, the control unit 20 checks whether the pattern material 401 has a disable pitch. More specifically, when a plurality of elements of the pattern material 401 select an element of interest and assume a new reference as a starting point for the selected element of interest, the control unit 20 checks for the vicinity of any end point of the presence reference vector. element. If control unit 20 determines that an element exists near any end of the reference vector, it determines that pattern data 401 has a disabled spacing. If control unit 20 decides that there is no element near the vicinity of any of the reference vectors, it determines that pattern data 401 does not have a disabled spacing.

If the control unit 20 decides that the decision pattern data 401 has a prohibited pitch, it proceeds to step S1110; otherwise, it proceeds to step S1112.

In step S1110, the control unit 20 removes elements near any end of the reference vector from the pattern material 401, and temporarily stores the information on the removed elements in the cache memory.

In step S1112, the control unit 20 performs the decision of step S1108 on all the elements (a plurality of elements of the pattern material 401 that have not been removed in step S1110).

If the control unit 20 decides that the decision of step S1108 has been performed on all elements, the process proceeds to step S1114; otherwise, the process returns to step S1108.

In step S1114, the control unit 20 generates the i-th pattern material (the i-th data generating step). More specifically, if i=1, the control unit 20 determines the pattern material obtained by removing the elements near the end points of all the reference vectors from the pattern material 401 as the i-th pattern material. If The control unit 20 determines the pattern data obtained by removing the elements near the end points of all the reference vectors from the (i-1)th pattern data as the i-th pattern material.

In step S1116, the control unit 20 newly sets the value i obtained by adding 1 to the reference number i of the pattern data.

In step S1118, the control unit 20 calculates the P map 413. More specifically, the control unit 20 calculates the P map 413 as a preliminary step of inserting (configuring) the auxiliary pattern in the pattern material 401. In step S1118, the function 412 is set based on all of the elements in the i-th pattern material. In other words, the function 412 is set by performing a predetermined method for all of the elements in the i-th pattern material (e.g., by magnifying the magnification), thereby calculating the P map 413. Since the mask function obtained from step S1102 is different from the mask function obtained from step S1118, it is necessary to calculate different P maps 413 in steps S1102 and S1118.

In step S1120, the control unit 20 generates the mask data 410 by inserting (configuring) the auxiliary pattern. More specifically, based on the P map 413 calculated in step S1118, the auxiliary pattern is inserted (configured) in regions that appear to be higher than the predetermined threshold value and correspond to the peak position. The control unit 20 then determines the information obtained as information on the auxiliary pattern in the mask data 410 as the new mask data 410. At this time, the control unit 20 can display the mask material 410 instead of the pattern material 401 on the display unit 30.

In step S1122, the control unit 20 checks whether there is an element removed from the pattern material 401 by referring to the cache memory.

If the control unit 20 determines that there is an element removed from the pattern material 401, it proceeds to step S1124; otherwise, the method ends.

In step S1124, the control unit 20 generates a pattern material 401 including an element removed when the i-th pattern material is generated as a new process target (second data generating step).

An example of dividing the pattern material 401 using the P image 413 will be explained. It is assumed that the P-image calculation information piece is identical to the fifth embodiment. The case where the pattern data 401 shown in Fig. 22A is a process target is considered. The pattern material 401 shown in Fig. 22A has three contact windows CP1 to CP3. The size (diameter) of each of the contact windows CP1 to CP3 is 120 nm.

The contact window CP2 is separated from the contact window CP1 by -280 nm in the y direction. The contact window CP3 is separated from the contact window CP2 by 225 nm in the x direction, and the contact window CP3 is separated from the contact window CP2 by -225 nm in the y direction.

The control unit 20 calculates the P map 413 by setting one element (i.e., one of the three contact windows CP1 to CP3) as the mask function 412. In this embodiment, the contact window CP1 is set as the mask function 412. At the position (±280, 0) and (0, ±280) on the mask, the P map 413 has a positive peak. And at positions (±225, 225) and (±225, -225) on the mask, the P map 413 has a negative peak.

Control unit 20 indicates a reference vector that represents, for example, the disable spacing of P-map 413. At this time, the four reference vectors are (225, 225), (225, -225), (-225, 225), and (-225, -225).

The control unit 20 selects the contact window (element) CP2 as the element of interest, assuming that the pattern material 401 shown in Fig. 22A is used as the process target. In this case, assuming that the position of the selected contact window CP2 is set as the attention element as the attention element as the starting point, the contact window (element) CP3 exists at one end point close to the reference vector. Therefore, the contact windows CP2 and CP3 have a disabled pitch relationship.

To cancel this state, the control unit 20 removes the contact window (element) CP3 close to one of the end points of the reference vector from the pattern material 401 shown in Fig. 22A to generate the first pattern material shown in the circle 22B. By this operation, the pattern material 401 shown in Fig. 22C is divided into the first pattern material shown in Fig. 22B and the second pattern material shown in Fig. 22C. This split produces mask data for two masks without any disabled spacing.

As explained in the fifth and ninth embodiments, the auxiliary pattern is inserted (configured) based on the P map 413 to improve the imaging performance of the mask. Therefore, compared with the simple double exposure, the insertion (configuration) of the optimum auxiliary pattern in the first pattern data shown in FIG. 22B and the second pattern data shown in FIG. 22C has been produced as shown in FIGS. 22D and 22E. Pattern data to improve imaging performance.

When the mask data shown in Figs. 22D and 22E is input to the EB drawing device, two masks are fabricated based on them. When the double exposure is performed using the two masks, the exposure is performed using the same mask as that of the pattern shown in Fig. 22A, and the contact windows CP1 to CP3 of higher precision can be formed.

<Twelfth Embodiment>

The optimization of the effective light source will be explained in the twelfth embodiment. In optimizing the effective light source, it is only necessary to judge the position of the element on the P map 413 (the area appearing to be equal to or greater than the value of the predetermined threshold) to match the element of the pattern data 401.

It is assumed that the P-image calculation information pieces other than the effective light source information 402 are identical to the fifth embodiment. As shown in FIG. 23A, the effective light source for pattern data (target pattern) 401 having three contact windows CP11 to CP13 is considered to be optimized. Three contact windows CP11 to CP13 are prepared in such a manner that the pitch dd is 300 nm. The size of each of the contact windows CP11 to CP13 is 120.

Figure 23B is a graph showing the effective source initial value (effective source information 402). In Fig. 23B, a white circular line indicates σ = 1, and a white area indicates a light irradiation portion. The aperture coordinate system is normalized so that the distance from the center of the circle to the center of each pole (light-irradiating portion) is set to 0.45 in the x direction, and is set to 0.45 in the y direction, and the respective poles are set (light-irradiating portion) The diameter of 0.3 is 0.3.

Based on the initial value of the effective light source shown in Fig. 23B, the control unit 20 calculates the P map 413 shown in Fig. 23c. The P map 413 shown in Fig. 23c has a positive peak at positions (0, ±300) and (±300, 0). The P map 413 shown in Fig. 23C is adapted to be based on the mask of the pattern material shown in Fig. 23A. This is because the pitch dd between adjacent contact windows on the mask based on the pattern material 401 shown in FIG. 23A is 300 nm.

The control unit 20 calculates a new P map 413 by resetting the mask function 412 (eg, by setting the mask function 412 as the target pattern itself). When the auxiliary pattern is inserted (configured) in a region which is equal to or larger than the predetermined threshold value and corresponds to the peak position on the P map 413, the mask material 810 as shown in FIG. 23D can be obtained. The masks based on the mask 410 shown in Fig. 23D are used, so that the contact windows CP11 to CP13 are formed with high precision.

24 is a flow chart for explaining a process for generating a mask 410 by mask generation of a program 414.

In step S1202, the control unit 20 sets the effective light source information 402.

In step S1204, the control unit 20 sets the mask function 412. It is to be noted that the mask function is not set based on the overall target pattern but based on one element of the target pattern. The mask function 412 is set by executing a predetermined process for one element (e.g., magnifying the magnification at a reduced magnification).

In step S1206, the control unit 20 calculates the mask function 412 based on the mask function 412 in step S1204.

In step S1208, the control unit 20 matches the P map 413 and the contact windows CP11 to CP13 as a desired pattern to be transferred by exposure.

In step S1210, the control unit 20 determines whether the contact windows CP11 to CP13 are suitable as a desired pattern that matches the peak on the P map 413 (each region that appears equal to or greater than the value of the predetermined threshold). If the control unit 20 determines the contact windows CP11 to CP13 as the desired pattern of the matching peaks, the process proceeds to step S1212. If the control unit 20 determines that the contact windows CP11 to CP13 as the desired pattern do not match the peak on the P map 413, the flow returns to step S1202.

In step S1212, the control unit 20 changes the mask function 412. Although the mask function 412 is set by focusing on one element of the target pattern in step S1204, all elements of the target pattern are set as the mask function 412. For this reason, the mask function 412 is set by performing a predetermined process for all elements of the target pattern, such as magnifying them at a reduced magnification.

In step S1214, the control unit 20 calculates the P map 413 based on the mask function 412 set in step S1212.

In step S1216, the control unit 20 inserts (configures) the auxiliary pattern based on the P map 413 calculated in step S1214 to generate mask material, and ends the method there.

In order to optimize the effective light source, steps S1202 to S1210 shown in Fig. 24 must be repeated (i.e., looped). The initial setting of the effective light source (effective light source information 402) is important to quickly complete the loop of steps S1201 to S1210. A method of simply calculating the initial setting effective light source, which can quickly complete the loop of steps S1201 to S1210 in a short period of time, will be explained below.

The light diffracted by the mask pattern forms a diffracted light distribution on the pupil plane of the projection optical system. As described above, let (f, g) be the amplitude of the diffracted light. As described above, the coordinates (f, g) on the pupil plane of the projection optical system are also normalized by assuming that the pupil size (the pupil diameter) of the projection optical system is 1. Let the ring (f-f', g-g') be a function that makes the position within the circle of radius 1 and the center of (f', g') be 1, and the other positions are zero. Let w(f, g) be the weighting function of the diffracted light.

First, the control unit 20 calculates the following formula:

S _raw (f,g)=∫∫w(f,g)a(f,g)circ(f-f',q-g')df'dg'...(35)

Where ∣f∣ 2 and ∣g'∣ 2.

Next, the control unit 20 calculates the following formula:

S(f,q)=S _raw (f,g)circ(f,g) ...(36)

Finally, the control unit 20 determines S(f, g) calculated by the equation (36) as the set value of the effective light source.

For example, consider the pattern material 401 as shown in FIG. 25A, in which the five-column and five-row contact window patterns are two-dimensionally arranged in a circular shape of 300 nm. In Fig. 25A, the ordinate indicates the y coordinate (unit: nm) on the surface of the mask, and the abscissa indicates the y coordinate (unit: nm) on the surface of the mask. The twelfth embodiment also assumes a case where a projection optical system having an NA of 0.73 (corresponding to NA information 403) and an exposure wavelength of 248 nm (corresponding to λ information 404) is used.

Based on equations (35) and (36), control unit 20 calculates a function S(f, g) that describes the effective source. Figure 25B shows the effective light source as described by the control unit 20 as described by the function S(f, g). In this embodiment, it is assumed that the weighting function w(f, g) is a quartic function which satisfies (0, 0) = 0.1 and w(2, 2) = 1. In FIG. 25B, the ordinate indicates the coherence factor σ in the x direction, and the abscissa indicates the coherence factor σ in the y direction.

Referring to Figure 25B, the effective light source described by the function S(f, g) is continuously changed. The effective light source shown in Figure 25B is close to the effective light source shown in Figure 23B. Therefore, the effective light source shown in FIG. 25B is applied as the initial value (set value of the effective light source) of the effective light source information 402 set in step S1202 in the loop of steps S1202 to S1210.

<Thirteenth Embodiment>

An exposure apparatus 100 that manufactures the mask 130 to perform an exposure method using the mask material 410 generated based on one of the above embodiments will be described in the thirteenth embodiment. It is to be noted that FIG. 26 is a schematic block diagram showing the configuration of the exposure apparatus 100.

The exposure apparatus 100 is an immersion exposure apparatus that transfers a pattern of the mask 130 onto the wafer 150 by using a step and scanning method via the liquid LW supplied between the projection optical system 140 and the wafer 150. However, the exposure apparatus 100 may employ a step and scan method or other exposure method.

As shown in FIG. 26, the exposure apparatus 100 includes a light source 110, an illumination optical system 120, a mask stage 135 for providing a mask 130, a projection optical system 140, a wafer stage 155 for setting a wafer 150, and a liquid supply/recycling. Unit 160, as well as primary control system 170. The light source 110 and the illumination optical system 120 constitute a lighting device that illuminates a mask 130 on which a circuit pattern to be transferred is formed.

Light source 110 is an excimer laser such as an ArF excimer laser having a wavelength of about 193 nm or a KrF excimer laser having a wavelength of about 248 nm. However, the kind and number of the light sources 110 are not particularly limited. For example, an F ₂ laser having a wavelength of about 157 nm can also be used as the light source 110.

Illumination optics 120 illuminates mask 130 with light from light source 110. In this embodiment, the illumination optical system 120 includes a beam shaping optical system 121, a focusing optical system 122, a polarization control unit 123, an optical integrator 124, and an aperture stop 125. The illumination optical system 120 also includes a concentrating lens 126, a curved mirror 127, a mask vane 128, and an imaging lens 129. Illumination optics 120 can implement various illumination modes, such as the conventional illumination and modified illumination (such as quadrupole illumination and dipole illumination) shown in Figures 4A and 14A.

For example, the beam shaping optical system 121 is a beam amplifier including a plurality of cylindrical lenses. The beam shaping optical system 121 converts the horizontal-to-vertical ratio of the cross-sectional shape of the collimated light from the light source 110 into a predetermined value (e.g., converts the cross-sectional shape from a rectangle to a square). In this embodiment, beam shaping optics 121 shapes the light from source 110 to the desired size and divergence angle of illumination optical integrator 124.

Focusing optics 122 includes a plurality of optical elements and effectively directs light shaped by beam shaping optics 121 to optical integrator 124. Focusing optics 122 includes, for example, a zoom lens system and adjusts the shape and angle of light entering optical integrator 124.

The polarization control unit 123 includes, for example, a polarization element, and is set at a conjugate position close to the pupil plane 142 of the projection optical system 140. The polarization control unit 123 controls the polarization state of a predetermined region of the effective light source formed by the pupil plane 142 of the projection optical system 140.

The optical integrator 124 has a function of uniformly illuminating light that illuminates the mask 130, converts the angular distribution of its incident light into a positional distribution, and outputs the resulting light. The optical integrator 124 is, for example, a fly-eye lens having a Fourier-converted relationship between its incident surface and the exit surface. The fly eye lens is formed by combining a plurality of rod lenses (i.e., microlens elements). However, the optical integrator 124 is not particularly limited to a fly-eye lens, and may be, for example, a cylindrical lens array plate in which the optical rod and the diffraction grating are orthogonally arranged to each other.

The aperture stop 125 is positioned adjacent the exit surface of the optical integrator 124 and near the conjugate of the effective source formed on the pupil plane 142 of the projection optical system 140. The aperture shape of the aperture stop 125 corresponds to the light intensity distribution (i.e., the effective light source) formed on the pupil plane of the projection optical system. In other words, aperture stop 125 controls the effective source. The aperture stop 125 can be switched according to the illumination mode. Without aperture stop, in the previous stage of optical integrator 124, an effective source can be formed by setting diffractive optical elements (such as CGH (computer generated hologram)) and 稜鏡 (such as pyramid).

The concentrating lens 126 converges to form an exiting surface proximate to the exit surface of the optical integrator 124 and through the aperture stop 125, and to uniformly illuminate the shroud blade 128 via the curved mirror 127.

The mask vanes 128 are positioned adjacent the conjugate position of the mask 130, and the shroud blades 128 are formed from a plurality of movable visors. The mask vanes 128 form an approximately rectangular opening that corresponds to the active area of the projection optics 140. The light beam passing through the mask vane 128 is used as illumination light for the illumination mask 130.

On the mask 130, the imaging lens 129 forms an image of the light beam that passes through the mask vanes 128.

The mask 130 is manufactured based on the mask data generated by the processing device 1 (mask generation program) by a manufacturing device such as an EB drawing device, and the mask 130 has a circuit pattern to be transferred and an auxiliary pattern. The pattern of the mask 130 may include a pattern different from the mask pattern produced by the mask generating program. The mask 130 is supported and driven by the mask table 135. The diffracted light generated by the mask 130 is projected onto the wafer 150 via the projection optical system 140. The mask 130 and the wafer 150 are set to have an optically conjugated relationship. Due to the stepping and scanning method of the exposure apparatus 100, the circuit pattern to be transferred of the mask 130 is transferred onto the wafer 150 by synchronously scanning them. When the exposure apparatus 100 takes the step and repeat method, it performs exposure when the mask 130 and the wafer 150 are stationary.

The mask station 135 supports the mask 130 via the mask chuck, and the mask station is coupled to a drive mechanism (not shown). The driving mechanism (not shown) is formed, for example, by a linear motor, and drives the mask table 135 in the X-, Y-, and Z-axis directions and in the direction of rotation of the individual axes. It is to be noted that the scanning direction of the mask 130 or the wafer 150 on the surface is defined as the Y-axis direction, the X-axis direction is defined perpendicular to the direction, and the surface perpendicular to the mask 130 or the wafer 150 is defined. The direction is the Z-axis direction.

Projection optics 140 projects the circuit pattern of mask 130 onto wafer 150. Projection optics 140 can be a refractive system, a reflective curved light system, or a reflective system. The final lens (final surface) of the projection optical system 140 is coated with a coating to reduce the effect of the liquid LW provided by the liquid supply/recovery unit 160 (for protection).

The wafer 150 is a substrate on which a circuit pattern of the mask 130 is projected (transferred). However, the wafer 150 may be replaced with a glass plate or other substrate. The wafer 150 is coated with a photoresist.

Like the mask stage 135, the wafer stage 155 supports the wafer 150 and moves in the X-, Y-, and Z-axis directions and in the direction of rotation about the individual axes using a linear motor.

The liquid supply/recovery unit 160 has a function of supplying a space between the liquid LW and the final lens (final surface) of the wafer 150 and the projection optical system 140. The liquid supply/recovery unit 160 also has a function of recovering the liquid LW that has been supplied to the space between the wafer 150 and the final lens of the projection optical system 140. A material having a high transmittance for relative exposure, a scale to prevent adhesion of the scale to the projection optical system 140 (on the final lens), and a method of matching the photoresist is selected as the liquid LW.

The primary control system 170 includes a CPU and memory, and controls the operation of the exposure device 100. For example, primary control system 170 is electrically coupled to mask station 135, wafer table 155, and liquid supply/recovery unit 160, and controls simultaneous scanning between mask table 135 and wafer table 155. For example, based on the scanning direction and speed of wafer table 155 during exposure, primary control system 170 also controls the supply of liquid, recovery, and switching between supply/recovery. In one of the above embodiments, primary control system 170 receives valid light source information, as well as controlling aperture stop, diffractive optical elements, and chirp to form an effective light source. The effective light source is transmitted from the processing device 1 to the exposure device 100 by user input or by connecting the processing device 1 to the exposure device 100 to input valid light source information to the primary control system 170 to allow data to communicate with each other. If the processing device 1 and the exposure device 100 are connected to allow data to communicate with each other, the exposure device 100 includes a known data receiving unit and the processing device 1 includes a known data transmitting unit.

Although the processing device 1 described above may be a computer disposed outside the exposure device 100, the primary control system 170 may have the function of the processing device 1 described above. In this case, the primary control system 170 can calculate the light intensity distribution (spatial image) formed on the surface of the wafer using the P operator for a short period of time. In other words, primary control system 170 can improve the speed of partial coherent imaging calculations, thus reducing the time spent on model-based RET. Therefore, the exposure apparatus 100 can optimize the exposure conditions (e.g., optimize the effective light source for the mask 130) for a short period of time, thus improving the throughput. The primary control system 170 can also produce masking material that is superior to the imaging performance using prior art of the P-image.

At the time of exposure, the light beam emitted by the light source 110 illuminates the mask 130 by the illumination optical system 120. The circuit pattern of the light-reflecting mask 130 being transmitted through the mask 130 forms an image on the wafer 150 via the liquid LW by the projection optical system 140. The exposure apparatus 100 has excellent imaging performance and can provide high throughput and good economical benefits to devices such as semiconductor devices, LCD devices, image sensing devices such as CCDs, and thin film magnetic heads. These devices are manufactured by a step of exposing a substrate (such as a wafer or a glass plate) coated with a photoresist (photosensitive agent) using an exposure apparatus 100, a step of developing an exposed substrate, and other known steps.

While the invention has been described with reference to the embodiments of the invention, it is understood that the invention is not limited to the disclosed embodiments. The following claims are intended to cover the broadest scope of

1. . . Processing equipment

10. . . Bus line

20. . . control unit

30. . . Display unit

40. . . Storage unit

50. . . Input unit

60. . . Media interface

70. . . Storage medium

100. . . Exposure equipment

110. . . light source

120. . . Lighting optical system

121. . . Beam shaping optical system

122. . . Concentrating optical system

123. . . Polarization control unit

124. . . Optical integrator

125. . . Aperture stop

126. . . Condenser lens

127. . . Curved mirror

128. . . Mask blade

129. . . Imaging lens

130. . . Mask

135. . . Masking station

140. . . Projection optical system

142. . . Optical plane

150. . . Wafer

155. . . Wafer table

160. . . Liquid supply/recovery unit

170. . . Main control system

401. . . Pattern data

402. . . Effective light source information

403. . . NA information

404. . . λ information

405. . . Aberration information

406. . . Polarized information

407. . . Photoresist information

408. . . P operator

409. . . Spatial image

410. . . Mask data

411. . . Spatial image calculation program

412. . . Mask function

413. . . P image

414. . . Mask generation program

1 is a schematic block diagram showing the configuration of a processing device 1 that performs a calculation method in accordance with the present invention.

2 is a schematic diagram showing a one-dimensional plane wave (orthogonal function system).

3 is a flow chart for explaining in detail a method of calculating a spatial image by the spatial image calculation program in the processing device 1 shown in FIG. 1.

4A to 4D are views for explaining a first embodiment according to the present invention, wherein FIG. 4A shows an effective light source used in the first embodiment, and FIG. 4B shows a mask material and a map used in the first embodiment. 4C shows the spatial image calculated by the spatial image calculation program, and FIG. 4D shows the spatial image calculated by the SOCS.

Figure 5 is a view for explaining a second embodiment according to the present invention, which shows a spatial image calculated by a spatial image calculation program when the projection optical system has aberration.

Figure 6 is a view for explaining a second embodiment according to the present invention, which shows a spatial image calculated by a spatial image calculation program when the illumination light is polarized.

7A to 7C are diagrams for explaining a third embodiment according to the present invention, wherein Fig. 7A shows mask data, and Figs. 7B and 7C show mask data after using mask data and OPC shown in Fig. 7A. , a spatial image calculated by a spatial image calculation program.

8A and 8B are diagrams for explaining a fourth embodiment according to the present invention, wherein FIG. 8A shows the relationship between the number and the square of the eigenvalues, and FIG. 8B shows the complete spatial image and the approximate spatial image (ie, by some The difference between the eigenvalue and the spatial image calculated by the eigenfunction).

9A to 9C are diagrams for explaining a fourth embodiment according to the present invention, wherein Fig. 9A shows an effective light source, Fig. 9B shows an uncompressed P operator, and Fig. 9C shows a compressed P operator.

Figure 10 is a block diagram showing the configuration of a processing apparatus in accordance with a fifth embodiment of the present invention.

11A to 11E are diagrams for explaining a fifth embodiment according to the present invention, wherein FIG. 11A shows an effective light source, FIG. 11B shows pattern data, FIG. 11C shows a P map, FIG. 11D shows mask data, and FIG. 11E shows Each region appears to be equal to or greater than the value of the P-image threshold.

Fig. 12 is a view showing an imaging performance of a mask having no auxiliary pattern, an imaging performance of a mask in which an auxiliary pattern is inserted according to the prior art, and a comparison result of an imaging performance of a mask in which an auxiliary pattern is inserted according to the fifth embodiment.

13A and 13B are diagrams for explaining a sixth embodiment according to the present invention, in which Fig. 13A shows pattern data and Fig. 13B shows P map.

14A to 14C are diagrams for explaining a seventh embodiment according to the present invention, wherein Fig. 14A shows an effective light source, Fig. 14B shows a P map, and Fig. 14C shows a mask.

15A to 15F are diagrams for explaining an eighth embodiment according to the present invention, which shows a P map.

16A and 16B are diagrams for explaining a ninth embodiment according to the present invention, wherein Fig. 16A shows a P map and Fig. 16B shows a mask material.

Figure 17 is a graph showing the comparison between the imaging performance of the mask of the mask data shown in Figure 11D (the fifth embodiment) and the imaging performance of the mask of the mask data shown in Figure 16B (the ninth embodiment). Chart.

Figure 18 is a diagram showing mask data according to a tenth embodiment of the present invention.

Figure 19 is a graph showing the comparison between the imaging performance of the mask of the mask data shown in Figure 16B (the ninth embodiment) and the imaging performance of the mask of the mask data shown in Figure 18 (the tenth embodiment). Chart.

Figure 20 is a view for explaining an eleventh embodiment according to the present invention, which shows that when an auxiliary pattern which is in phase with a desired pattern to be transferred by exposure is disposed at a position having a positive value on the P map The out-of-focus feature, and the out-of-focus feature when the auxiliary pattern in phase with the desired pattern to be transferred by exposure is disposed at a position having a negative value on the P map.

Figure 21 is a flow chart for explaining a method of generating pattern data without any prohibited pitch by a mask generating program.

22A to 22E are diagrams for explaining an eleventh embodiment according to the present invention, wherein FIG. 22A shows pattern data, circles 22B and 22c display mask data, and FIGS. 22D and 22E show mask data in which auxiliary patterns are inserted. .

23A to 23D are diagrams for explaining a twelfth embodiment according to the present invention, wherein Fig. 23A shows pattern data, Fig. 23B shows an effective light source, Fig. 23c shows a P map, and Fig. 23D shows mask data.

Figure 24 is a flow chart for explaining a mask generating method for generating a program by masking.

25A and 25B are diagrams for explaining a twelfth embodiment according to the present invention, in which FIG. 25A shows pattern data and FIG. 25B shows an effective light source.

Figure 26 is a schematic diagram showing the configuration of an exposure apparatus according to the present invention.

1. . . Processing equipment

10. . . Bus line

20. . . control unit

30. . . Display unit

40. . . Storage unit

50. . . Input unit

60. . . Media interface

70. . . Storage medium

401. . . Pattern data

402. . . Effective light source information

403. . . NA information

404. . . λ information

405. . . Aberration information

406. . . Polarized information

407. . . Photoresist information

408. . . P operator

409. . . Spatial image

410. . . Mask data

411. . . Spatial image calculation program

Claims (15)

A method of calculating a light intensity distribution formed on an image plane of a projection optical system, using an illumination optical system to illuminate a mask and projecting an image of the pattern of the mask to the image through the projection optical system On the substrate, the light intensity distribution is calculated by a computer, the calculation method comprising: a dividing step of dividing an effective light source formed on a pupil plane of the projection optical system into a plurality of point light sources; Generating a pupil function describing one pupil of the projection optical system for each of the plurality of point light sources by a movement amount according to respective positions of the point light sources, thereby generating a plurality of moving pupil functions; a step of defining a matrix by arranging each of the plurality of moving pupil functions, the plurality of moving pupil functions being generated in the generating step in each column or rows of the matrix; a first calculating step, executing the Defining a singular value decomposition of the matrix defined in the step, thereby calculating an eigenvalue and an eigenfunction; and a second calculation step based on The distribution of the light of the diffraction pattern of the mask, and the eigenvalue calculated in the first calculation step and the eigenfunctions, the calculation of the projected light intensity on the image plane of the optical system of distribution formed. The method of claim 1, wherein in the generating step, the pupil function is moved by a difference between a central position of the pupil of the projection optical system and a position of the point light sources. The method of claim 1, wherein the plurality of The pupil function includes information indicating at least one of: an aberration of the projection optical system, a polarization state of the light that illuminates the mask, a change in light intensity of one of the effective light sources, and a winding of the mask Shooting efficiency. The method of claim 1, wherein the plurality of moving pupil functions are one-dimensionally arranged in the generating step. A method for generating data for a pattern of a mask including an exposure device of a projection optical system by a computer, the generating method comprising: a dividing step of forming a pupil formed in the projection optical system An effective light source on the plane becomes a plurality of point light sources; a generating step of moving a light describing the pupil of the projection optical system for each of the plurality of point light sources by a movement amount according to each position of the point light sources a 瞳 function, thereby generating a plurality of moving pupil functions; a defining step of defining a matrix by arranging each of the plurality of moving pupil functions, the plurality of moving pupil functions in each column or row of the matrix Generating in the generating step; a first calculating step of performing singular value decomposition of the matrix defined in the defining step, thereby calculating an eigenvalue and an eigenfunction; and a second calculating step when inserting When the element of a target pattern is on an object plane of the projection optical system, based on the distribution of light diffracted by the target pattern and the calculation in the first calculation step The eigenvalue and the eigenfunction, calculate an image indicating that the elements affect each other; and a data generating step of generating the data of the mask based on the image calculated in the second calculating step . The method of claim 5, wherein in the data generating step, a region determined based on a threshold value of the image and a plurality of elements of the target pattern assuming that the data of the target pattern is a processing target When there is no match, the effective light source is reset, and the pattern of the pattern of the mask is generated based on the reset effective light source. The method of claim 5, wherein the data generating step comprises: a specifying step of assigning a reference vector to an area by an origin, the display being not less than the calculated in the second calculating step a value of a threshold value on the image; a first data generation step of selecting one of a plurality of elements of the target pattern, and removing the reference vector when the center of the element is assumed to be a starting point An element at a position that matches an endpoint of the reference vector, thereby generating a first pattern data; and a second data generation step of generating the element formed from the element removed in the first data generation step Two pattern materials. The method of claim 7, wherein in the data generating step, the first data generating step and the second data generating step are repeated. A storage medium storing a program for causing a computer to perform calculations when an illumination optical system is used to illuminate a mask and project an image of a pattern of the mask onto a substrate via a projection optical system a light intensity distribution formed on an image plane of the projection optical system, the program causing the computer to execute: a dividing step of dividing an effective light source formed on a pupil plane of the projection optical system into a plurality of point light sources; and generating a step of, for each position of the point light sources, by a movement amount for each of the plurality of points Point source movement describes a pupil function of one of the projection optical systems, thereby generating a plurality of moving pupil functions; a defining step of defining a matrix by arranging each of the plurality of moving pupil functions, A plurality of moving pupil functions are generated in the generating step in each column or rows of the matrix; a first calculating step of performing singular value decomposition of the matrix defined in the defining step, thereby calculating an eigenvalue a value and an eigenfunction; and a second calculating step based on the distribution of light diffracted by the pattern of the mask, and the eigenvalue and the eigenfunction calculated in the first calculating step, The light intensity distribution formed on the image plane of the projection optical system is calculated. A storage medium storing a program for causing a computer to execute processing for generating one of a pattern of a mask including an exposure device of a projection optical system, the program causing the computer to perform: a segmentation step, segmentation An effective light source on a pupil plane of the projection optical system becomes a plurality of point light sources; a generating step of describing the projection for each of the plurality of point source movements by a movement amount according to each position of the point light sources a pupil function of one of the optical systems, thereby generating a plurality of moving pupil functions; a defining step of defining a matrix by arranging the plurality of moving pupil functions, the plurality of moving pupils Function in each column or each of the matrix Generating in the generating step; a first calculating step of performing singular value decomposition of the matrix defined in the defining step, thereby calculating an eigenvalue and an eigenfunction; and a second calculating step Inserting an element of a target pattern onto an object plane of the projection optical system based on a distribution of light diffracted by the target pattern and the eigenvalue and the eigenfunction calculated in the first calculating step Calculating an image indicating that the elements affect each other; and a data generating step of generating data of the pattern of the mask based on the image calculated in the second calculating step. An exposure method comprising: a calculating step of calculating a shadow image of a mask of a mask onto a substrate by using an illumination optical system to illuminate a mask and projecting the image of the mask to a substrate via a projection optical system a light intensity distribution on an image plane; an adjustment step of adjusting an exposure condition based on the calculated light intensity distribution in the calculating step; and an exposure step of projecting the pattern of the mask after the adjusting step And the calculating step comprises a dividing step of dividing an effective light source formed on a pupil plane of the projection optical system into a plurality of point light sources; and generating a step according to each of the point light sources Positioning a displacement function describing a pupil of the projection optical system for each of the plurality of point light sources by a movement amount, thereby generating a plurality of moving pupil functions; a defining step of defining a matrix by arranging each of the plurality of moving pupil functions, the plurality of moving pupil functions being generated in the generating step in each column or rows of the matrix; a first calculating step, Performing a singular value decomposition of the matrix defined in the defining step, thereby calculating an eigenvalue and an eigenfunction, and a second calculating step, based on the distribution of light diffracted by the pattern of the mask And the eigenvalue calculated in the first calculating step and the eigenfunction, and calculating the light intensity distribution formed on the image plane of the projection optical system. A mask manufacturing method comprising: generating a pattern for a mask according to a production method defined in any one of claims 5 to 8; and fabricating the mask using the generated data. An exposure method comprising the steps of: manufacturing a mask according to the mask manufacturing method defined in claim 12; illuminating the manufactured mask; and patterning one of the masks via a projection optical system An image is projected onto a substrate. A method for calculating a transmission intersection coefficient in an exposure apparatus by a computer, the exposure apparatus illuminating a mask using an illumination optical system, and projecting an image of a pattern of the mask to the image via a projection optical system On the substrate, the calculation method comprises: a segmentation step, the segmentation is formed on one of the projection optical systems An effective light source on the surface becomes a plurality of point light sources; a generating step of moving a light describing the pupil of the projection optical system for each of the plurality of point light sources by a movement amount according to each position of the point light sources a 瞳 function, thereby generating a plurality of moving pupil functions; a defining step of defining a matrix by arranging each of the plurality of pupil functions, the plurality of moving pupil functions being in each column or rows of the matrix The generating step is generated; and a calculating step of calculating the transmission intersection coefficient based on the matrix defined in the defining step. The method of claim 14, further comprising the step of performing a singular value decomposition of the matrix describing the transmission intersection coefficient calculated in the calculating step, thereby calculating an eigenvalue and an eigenfunction .